Calculating Limits of Integration for Joint Distributions

sid9221
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http://dl.dropbox.com/u/33103477/Joint.png

This is my interpretation of the limits of integration can you tell me if this is correct and also how do you calculate these limit's. Cause I'm not completely sure how they're calculated.

\int_{0}^{1}\int_{1-y}^{1} ce^x e^y dx dy
 
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Yes, that is correct. Now what is the graph of that region?
Draw the lines x= 1, y= 1, x+ y= 1.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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