Maximizing Volume Formula for Given Box Dimensions and Cut Size

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Homework Statement


A box is given with a L = 1.414w and W = w and a cut size = x. Find the general formula for the maximum volume.

Homework Equations


L = 1.414w - 2x
W = w - 2x
H = x

The Attempt at a Solution


V = x(1.414w - 2x)(w - 2x)
V = 4x3 - 4.818x2w + 1.414w2
Apparently this isn't the general formula for max volume, so someone please help.
 
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Never mind guys. I figured it out.
 
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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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