Determine a so the area between the graph of the function and the x-axis is $\displaystyle \frac{100}{3}$:

$\displaystyle f(x)=|x^2-a^2|$

$\displaystyle a\in \left[ 0,10 \right]$

$\displaystyle 0\leq x\leq 10$

So i thought it would be good to use integrals.

$\displaystyle f(x)=-x^2+a^2$ , when $\displaystyle x^2+a^2<0$

$\displaystyle f(x)=x^2-a^2$ , when $\displaystyle x^2+a^2\geq0$

But how do i get the interval for the integrals?

Thanks!