hyperbolic triangle proof

May 2010
274
67
Los Angeles, California
Figure 3 on the next page shows the region \(\displaystyle \Delta\) that you're integrating over and where \(\displaystyle a\) and \(\displaystyle b\) are coming from. For \(\displaystyle y\), you're integrating from the top of the unit circle to infinity.
 
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May 2010
13
1
so is sqrt(1-x^2) just the top of the unit circle?
 
May 2010
274
67
Los Angeles, California
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?
 
May 2010
13
1
Its been 2 years since ive done any integration whatsover, ive forgotton most of the double/triple integrals
 
May 2010
13
1
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:
May 2010
274
67
Los Angeles, California
You should review double integration and in particular evaluating them through iteration. It'll all be clear after that.