Question

Find all values of k for which integral of x^2 from 2 to k =0 ?

`int_2^kx^2dx=0`

I have no idea how to do this and it is for a test tomorrow... I know that the answer is 2 but I don't understand why

Answer 1

See below. (This answer assumes that you have access to the Fundamental Theorem of Calculus.)

Explanation:

`int_2^k x^2 dx = [x^3/3]_2^k`

`= k^3/3-2^2/3`

`= (k^3-8)/3`

Set this equal to `0` and solve for `k`.