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Math Help - Double integrals, reversing the order of integration.

  1. #1
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    Double integrals, reversing the order of integration.

    Hi, I have been told to integrate the double integral sec x dx dy with the limits 0<y<1 and 0<x<cos^-1 y by first reversing the order of integration.

    The problem I am having is I can't quite understand yet how to alter these limits.

    I tried to change them and ended up with 0<y<cos x and cos^-1y < x < 0

    After trying to integrate with these new limits I was stumped when trying to work out y sec (cos x) - y sec 0.

    Any help would be greatly appreciated, thanks, Martin.
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  2. #2
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    Re: Double integrals, reversing the order of integration.

    Quote Originally Posted by mgrafton View Post
    Hi, I have been told to integrate the double integral sec x dx dy with the limits 0<y<1 and 0<x<cos^-1 y by first reversing the order of integration.

    The problem I am having is I can't quite understand yet how to alter these limits.

    I tried to change them and ended up with 0<y<cos x and cos^-1y < x < 0

    After trying to integrate with these new limits I was stumped when trying to work out y sec (cos x) - y sec 0.

    Any help would be greatly appreciated, thanks, Martin.
    Just to clarify, your integral is

    \int_{0}^{1}\int_{0}^{\cos^{-1}(y)}\sec(x)\,dx\,dy.

    Is that correct?
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