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Math Help - how to switch parameters for double integrals

  1. #1
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    how to switch parameters for double integrals

    This is probably very simple but I don't know why I am having trouble switching the order of integration and the parameters for double integrals.

    For example,

    if the x parameters are 0 and pi and the y parameters are 0 and sinx,

    how would i change the parameters so I express x as function of y and get two values for y boundaries
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  2. #2
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    The double integral

    \int_0^{\pi}\int_0^{\sin x}dy\,dx

    is equivalent to

    \int_0^1\int_{\arcsin y}^{\pi-\arcsin y}dx\,dy.

    Note that as x passes \pi/2, our formula for the inverse changes.
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  3. #3
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    Is there any other way this can be done without using arcsin?
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  4. #4
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    Quote Originally Posted by messianic View Post
    Is there any other way this can be done without using arcsin?
    Since y = sin x is one of the curves bounding the region the answer to your question is obviously no!
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