How do you find the average value of #f(x)=x^52x^32# as x varies between #[1,1]#?
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To find the average value of the function (f(x) = xTo find the average value of the function ( f(x)To find the average value of the function (f(x) = x^To find the average value of the function ( f(x) =To find the average value of the function (f(x) = x^5To find the average value of the function ( f(x) = xTo find the average value of the function (f(x) = x^5 To find the average value of the function ( f(x) = x^To find the average value of the function (f(x) = x^5  To find the average value of the function ( f(x) = x^5To find the average value of the function (f(x) = x^5  2To find the average value of the function ( f(x) = x^5 To find the average value of the function (f(x) = x^5  2xTo find the average value of the function ( f(x) = x^5  To find the average value of the function (f(x) = x^5  2x^To find the average value of the function ( f(x) = x^5  2To find the average value of the function (f(x) = x^5  2x^3To find the average value of the function ( f(x) = x^5  2xTo find the average value of the function (f(x) = x^5  2x^3 To find the average value of the function ( f(x) = x^5  2x^To find the average value of the function (f(x) = x^5  2x^3  To find the average value of the function ( f(x) = x^5  2x^3 To find the average value of the function (f(x) = x^5  2x^3  2To find the average value of the function ( f(x) = x^5  2x^3  2To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,To find the average value of the function ( f(x) = x^5  2x^3  2 \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as (To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]),To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), youTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you wouldTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would followTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow theseTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), weTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we useTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
1.To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formulaTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula forTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definiteTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integralTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the averageTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral ofTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average valueTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral of theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value ofTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral of the functionTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of aTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral of the function overTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a functionTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral of the function over theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function overTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral of the function over the givenTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over anTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:

Calculate the definite integral of the function over the given interval \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \textTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{AverageTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]). To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average valueTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]). 2To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} =To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
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[ \text{Average value} = \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
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[ \text{Average value} = \fracTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the resultTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result fromTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from stepTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{bTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  aTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 byTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the widthTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width ofTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \intTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{aTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, whichTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which isTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{bTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} fTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
MathemTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) ,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
MathematicallyTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dxTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the averageTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
whereTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average valueTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where (To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (fTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [aTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, bTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\textTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b]To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avgTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] )To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) isTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}})To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) ofTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the intervalTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval overTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (fTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over whichTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(xTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the functionTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x))To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function isTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) overTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is beingTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluatedTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the intervalTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
ForTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the givenTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given functionTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( fTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) canTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) =To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be foundTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found usingTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formulaTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5 To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ fTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\textTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3 To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avgTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} =To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 )To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) andTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \fracTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{bTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{baTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \intTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]\To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), weTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{bTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ aTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} fTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a =To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(xTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x)To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) ,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dxTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quadTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad bTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b =To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
whereTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a)To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) andTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
PlTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
PluggingTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (bTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging theseTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b)To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these valuesTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) areTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values intoTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lowerTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formulaTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower andTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upperTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, weTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limitsTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we getTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits ofTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the intervalTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectivelyTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \textTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
GivenTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{AverageTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average valueTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (aTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} =To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \fracTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1)To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) andTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b =To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1 To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1),To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \intTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), andTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the functionTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (fTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x)To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) =To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2)To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (fTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) ,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(xTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
NowTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x))To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, weTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) overTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrateTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over theTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the intervalTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \intTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \intTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1}To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (xTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5 To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5 To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2)To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) ,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2)To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
AfterTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) ,To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After findingTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dxTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx =To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the resultTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result ofTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \leftTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of thisTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integralTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \fracTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, weTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divideTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide itTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it byTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the widthTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6} To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the intervalTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \fracTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval (\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2))To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) toTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the averageTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4} To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average valueTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value ofTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2xTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the functionTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \rightTo find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over theTo find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval \To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([1,To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1}^{To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([1,1To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1}^{1To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([1,1]\To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1}^{1}To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([1,1]).To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1}^{1} \To find the average value of the function (f(x) = x^5  2x^3  2) as (x) varies between ([1,1]), you would follow these steps:
 Calculate the definite integral of the function over the given interval ([1,1]).
 Divide the result from step 1 by the width of the interval, which is (2).
Mathematically, the average value (f_{\text{avg}}) of (f(x)) over the interval ([1,1]) can be found using the formula:
[ f_{\text{avg}} = \frac{1}{ba} \int_{a}^{b} f(x) , dx ]
where (a) and (b) are the lower and upper limits of the interval respectively.
Given (a = 1) and (b = 1), and the function (f(x) = x^5  2x^3  2), we can integrate (f(x)) over the interval ([1,1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx ]
After finding the result of this integral, we divide it by the width of the interval ((2)) to obtain the average value of the function over the interval ([1,1]).To find the average value of the function ( f(x) = x^5  2x^3  2 ) as ( x ) varies between ([1, 1]), we use the formula for the average value of a function over an interval:
[ \text{Average value} = \frac{1}{b  a} \int_{a}^{b} f(x) , dx ]
where ( [a, b] ) is the interval over which the function is being evaluated.
For the given function ( f(x) = x^5  2x^3  2 ) and the interval ([1, 1]), we have:
[ a = 1, \quad b = 1 ]
Plugging these values into the formula, we get:
[ \text{Average value} = \frac{1}{1  (1)} \int_{1}^{1} (x^5  2x^3  2) , dx ]
Now, we integrate the function over the interval ([1, 1]):
[ \int_{1}^{1} (x^5  2x^3  2) , dx = \left[ \frac{x^6}{6}  \frac{2x^4}{4}  2x \right]_{1}^{1} ]
[ = \left( \frac{1}{6}  \frac{2}{4}  2 \right)  \left( \frac{(1)^6}{6}  \frac{2(1)^4}{4}  2(1) \right) ]
[ = \left( \frac{1}{6}  \frac{1}{2}  2 \right)  \left( \frac{1}{6}  \frac{1}{2} + 2 \right) ]
[ = \left( \frac{11}{6} \right)  \left( \frac{11}{6} \right) ]
[ = 0 ]
Therefore, the average value of the function ( f(x) = x^5  2x^3  2 ) over the interval ([1, 1]) is ( 0 ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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