# Area between the graph of the function and x-axis

• Apr 13th 2011, 12:17 PM
mechaniac
Area between the graph of the function and x-axis
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!
• Apr 13th 2011, 12:36 PM
Plato
Quote:

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 $\int_0^a {\left( {a^2 - x^2 } \right)dx = \frac{{50}}
{3}}$