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Math Help - solving a double integral

  1. #1
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    solving a double integral

    int (1/(4-r^2)^0.5) dr dx, r=0 to 2sinx, x=0 to 2pi

    I'm stuck at

    int (arcsin(sin(x))) dx, x=0 to 2pi

    Should i have done a change in variables somewhere?
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  2. #2
    A Plied Mathematician
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    Try plotting the function, and I think you'll see what needs to be done.
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  3. #3
    MHF Contributor

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    For x between -\pi/2 and \pi/2, arcsin(sin(x))= x. For x between \pi/2 and 3\pi/2, arcsin(sin(x))= x- \pi.
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  4. #4
    A Plied Mathematician
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    I think it's more this:

    \sin^{-1}(\sin(x))=\begin{cases}x,\quad& 0\le x\le\pi/2\\<br />
\pi-x,\quad& \pi/2\le x\le 3\pi/2\\<br />
x-2\pi,\quad& 3\pi/2\le x\le 2\pi\end{cases}.
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