Solving a Red Equation: Where Did I Go Wrong?

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Homework Statement



Hey guys.
I have this equation in red (in the pic) which I need to solve

http://img241.imageshack.us/img241/9323/scan0004n.jpg

As you can see I came up with with 2*t0.
When I solve it in Matematica I come up with t2=t0 without the 2.
Also, their answer in the book is also only t0.
Can someone please tell me where is my mistake please?

Thanks.


Homework Equations





The Attempt at a Solution

 
Last edited by a moderator:
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Everything looks good until the final line. Why have you suddenly changed from T = t2 to T = 2t0? What is t0? How does it relate to t2?
 

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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