Area between the graph of the function and x-axis

**mechaniac** · April 13th 2011, 11:17 AM

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

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

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

$0\leq x\leq 10$

So i thought it would be good to use integrals.

$f(x)=-x^2+a^2$ , when $x^2+a^2<0$
$f(x)=x^2-a^2$ , when $x^2+a^2\geq0$

But how do i get the interval for the integrals?

Thanks!

**Plato** · April 13th 2011, 11:36 AM

Originally Posted by mechaniac

Determine a so the area between the graph of the function and the x-axis is $\frac{100}{3}$ :
$f(x)=|x^2-a^2|$
$a\in \left[ 0,10 \right]$
$0\leq x\leq 10$

That is equivalent finding $a$ so that $\int_0^a {\left( {a^2 - x^2 } \right)dx = \frac{{50}}<br /> {3}}$

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