Calculus problem on volume of vectors. thanks

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Homework Statement



three dimensional coordinate systems. vectors.
a) let W br yhe solid region consisting of all the point p(x,y,z) satisfying the following 4 conditions:i) the distance from P to the point (4,2,6) is at lewast twice the distance forom P to the point (1,2,3) ii x>or = 0, iii) y> or = 2 iv) y> or = z. find the volume of solid W


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The Attempt at a Solution

 
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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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