Solving Homework: Can You Find the Right Answer?

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Homework Statement


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Homework Equations


The Attempt at a Solution


The answer is 16, but I get 12 only

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The integrand becomes u^2. one 'u' from the xdx and the other from the original substitution.
 
Oster said:
The integrand becomes u^2. one 'u' from the xdx and the other from the original substitution.

Oh my god. How come I can't even notice such a silly mistake.
 
lol. happens to me a lot.
 

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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