Compute the integral by reversing the order of integration

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Homework Statement



The problem is in the link.

http://img26.imageshack.us/i/80222189.png/

Homework Equations



None.

The Attempt at a Solution



I did not get far. The only thing I got was the graph. Here is the link to that.

http://img813.imageshack.us/f/graphv.png/

I am suppose to reverse the order of integration. However, I am having trouble finding the limits for x and y.

I spent around 8 hours thinking about this problem -.-

Can anyone please help me with this problem?

Thanks.
 
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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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