Having troubles getting this derivative

bmed90 · 2010-10-13T00:59:09+00:00

Homework Statement find dx/dt and dy/dt Homework Equations x= sin(t)-tcos(t) y=cos(t)+tsin(t) The Attempt at a Solution dx/dt= cos(t)-(-tsin(t)) = cos(t)+tsint dy/dt=-sin(t)+tcost

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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The Attempt at a Solution

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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