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Math Help - Area between the graph of the function and x-axis

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by mechaniac View Post
    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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