Question

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`

Watch this problem solved here.