How do you find the Riemann sum associated with #f(x)=3x^2 +6#, n=3 and the partition of [0,6]?
Rewrite further to taste.
Perhaps you'd prefer
By signing up, you agree to our Terms of Service and Privacy Policy
To find the Riemann sum associated with ( f(x) = 3x^2 + 6 ), ( n = 3 ), and the partition of ( [0,6] ), follow these steps:

Calculate the width of each subinterval, denoted as ( \Delta x ), using the formula: [ \Delta x = \frac{{b  a}}{n} ] where ( a = 0 ) (the lower limit of the interval), ( b = 6 ) (the upper limit of the interval), and ( n = 3 ).

Calculate the endpoints of each subinterval. Since ( n = 3 ), you'll have four endpoints: ( x_0 = 0 ), ( x_1 = 2 ), ( x_2 = 4 ), and ( x_3 = 6 ).

Evaluate ( f(x) ) at each endpoint: [ f(x_0) = f(0), \quad f(x_1) = f(2), \quad f(x_2) = f(4), \quad \text{and} \quad f(x_3) = f(6) ]

Use the Riemann sum formula to calculate the sum: [ \text{Riemann sum} = \Delta x \left[ f(x_0) + f(x_1) + f(x_2) + f(x_3) \right] ]

Substitute the values of ( \Delta x ) and the function evaluations into the formula and compute the sum.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
 How do you estimate the area under the curve #f(x)=x^29# in the interval [3, 3] with n = 6 using the trapezoidal rule?
 When do you use the trapezoidal rule?
 How do you use the trapezoidal rule with n=4 to approximate the area between the curve #y=sqrt(x+1)# from 1 to 3?
 Use Riemann sums to evaluate? : #int_0^(pi/2) \ sinx \ dx# ?
 Integrate (1)/(sqrt(1x^2)) from 1 to 1?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7