How do you find the area under the graph of #f(x)=x^2# on the interval #[-3,3]# ?

Answer 1

This is an integration problem. We will find the area under the curve #x^2# over the interval [-3,3]. This included both -3 and 3 because of the square brackets.

The integration of #x^2# is found by incrementing the power to #3# and using #3# as the denominator.

#int_a^bx^ndx=[x^(n+1)/(n+1)]_a^b=b^(n+1)/(n+1)-a^(n+1)/(n+1)#

#int_-3^3x^2 dx=[x^3/3]_-3^3=[(3)^3/3-(-3)^3/3]=27/3-(-27)/3=27/3+27/3=9+9=18#

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Answer 2

Luke Alvarez

To find the area under the graph of ( f(x) = x^2 ) on the interval ([-3, 3]), you can use definite integration. You integrate ( f(x) ) with respect to ( x ) from (-3) to (3), which means finding the integral of ( x^2 ) from (-3) to (3). This can be represented mathematically as:

[ \int_{-3}^{3} x^2 , dx ]

Evaluating this integral will give you the area under the graph of ( f(x) = x^2 ) on the interval ([-3, 3]).

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Answer from HIX Tutor

When evaluating a one-sided 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.