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Math Help - hyperbolic triangle proof

  1. #1
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    hyperbolic triangle proof

    I wasnt sure where to post this but im having trouble understanding a part of this proof, the integration part, could anyone explain to me where the intervals infinite and sqrt(1-x^2), and beta, pi - alpha come from in the integrals on the proof on page 3 of: http://www.maths.manchester.ac.uk/~c.../lecture07.pdf
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  2. #2
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    Figure 3 on the next page shows the region \Delta that you're integrating over and where a and b are coming from. For y, you're integrating from the top of the unit circle to infinity.
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  3. #3
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    so is sqrt(1-x^2) just the top of the unit circle?
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  4. #4
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    This is the standard way to evaluate a double integral by iteration. Are you familair with double and triple integration over two and three dimensional regions?
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  5. #5
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    Its been 2 years since ive done any integration whatsover, ive forgotton most of the double/triple integrals
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  6. #6
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    i remember how to integrate double integrals and everything, its just i don't understand why there is sqrt(1-x^2) ive looked in my old textbook for calculus and it doesnt have anything there

    hmmm i'm not sure if im getting it right, is it because like the equation of a circle x^2 + y^2 = r but r = 1 so to get y we have sqrt(1-x^2), i know this isnt exactly right but am i on the right lines
    Last edited by Purslow; May 19th 2010 at 05:18 PM. Reason: inspiration
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  7. #7
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    You should review double integration and in particular evaluating them through iteration. It'll all be clear after that.
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  8. #8
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    ok thanks
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