Parametrizing a Circle: Solving |z-z_o| = r for z(t)

squaremeplz · 2009-05-08T01:03:53+00:00

Homework Statement trying to parametrize |z - 2 + i | = 3 Homework Equations |z - z_o| = r The Attempt at a Solution z(t) = 2 + i + 3e^(it) im not sure if 2 + i is correct, or 2 - i.

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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Homework Statement

Homework Equations

The Attempt at a Solution

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

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