Proofs for Sets: Expert Help and Tips for Math Homework

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Homework Statement



hopefully the writing is readable:
http://i.imgur.com/VJ8vN.jpg

All three if possible.

Homework Equations



none

The Attempt at a Solution



To be completely honest, I missed that whole week of lectures due to personal problems and I've had no chance to talk to an instructor or a classmate for some notes before this is due. I'm perfectly fine with just tiny tips here and there.

http://i.imgur.com/4AknY.jpg

My lame attempt at solving the first.
 
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what have I done?
 
I was able to figure out the first two I believe. But at the moment I seem to be stuck on the 3rd. Would it be alright if I was to list all the options a and b have in order for ab=4 and then write that we can see they all work?

This is for a Math 273 course.
 
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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