Solving Integrals: Can't Get the Right Answer?

sntawkin
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If you let the first attatchment be true then to find the second attachment you need to...

There was a first part to this question and I got it right. Now I try the equation and I get the integral from 11 to 9.5 = 10 + -9 + 2. Then f(x) would equal 3. If you enter that into ((9(f(x) -2) then you get 25 but that is wrong. then i tried putting 10, -9 and 2 into the equation and adding them to get 21 but that is wrong as well. I don't know where to go from here.
 

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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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