(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int_{-2}^{2}\left(\frac{2-x}{2+x}\right)^{1/2}\hspace{1mm}dx[/tex]

2. Relevant equations

[tex]B(p,q) = \int_0^{\infty}\frac{y^{p-1}}{(1+y)^{p+q}}\hspace{1mm}dy[/tex]

3. The attempt at a solution

I am completely stuck on this one, just a total mental block. The answer in the book says:

"First put u = x + 2. Then put u = 4t. Answer = [tex]2\pi[/tex]"

I'll take you through what I done, but I got nowhere near the Beta function form I require:

[tex]u = x + 2\hspace{1mm}=>\hspace{1mm}4 - u = 2 - x[/tex]

Also: du = dx. So:

[tex]\int_{0}^{4}\left(\frac{4-u}{u}\right)^{1/2}\hspace{1mm}du[/tex]

So now I thought to do the second part ( set u = 4t ):

[tex]u = 4t => du = 4 dt[/tex]

[tex]4\int_{0}^{1}\left(\frac{4-4t}{4t}\right)^{1/2}\hspace{1mm}dt[/tex]

And I take out four as a common factor:

[tex]4\int_{0}^{1}\left(\frac{1-t}{t}\right)^{1/2}\hspace{1mm}dt[/tex]

I don't have a clue on how to proceed, it is nowhere near the equation I need, I'm not sure how to get rid of the square root, or even "turn it upside down", but even then that doesn't work because I have 1 - t and I require something like 1 + t. I would really appreciate any help on this, thank you for your time.

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# Homework Help: Beta Function Problem

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