Mistake in provided solutions?

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Homework Statement



The problem is attached in the picture.


The Attempt at a Solution



If you refer to line 2 of the working, they substituted x with 'b' instead of y with 'b' since the first integral is with respect to y.

Is this a mistake or is there something more?
 

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Looks to me like they're substituting x=a and x=0 on line 2, just like you'd expect.
 
The first integral is NOT with respect to y, it is with respect to x.
 
I got a different answer when I integrated with respect to y first... I am missing the additional sqrt(b) term..
 
Then you made a mistake somewhere :-)
 
clamtrox said:
Then you made a mistake somewhere :-)

You are right, I saw my mistake.. Thanks btw!
 

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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