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

## ${\int}_{2}^{k} {x}^{2} \mathrm{dx} = 0$ 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

Apr 20, 2017

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

#### Explanation:

${\int}_{2}^{k} {x}^{2} \mathrm{dx} = {\left[{x}^{3} / 3\right]}_{2}^{k}$

$= {k}^{3} / 3 - {2}^{2} / 3$

$= \frac{{k}^{3} - 8}{3}$

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