How to calculate $\int_0^{2\pi} \sqrt{1 - \sin^2 \theta}\;\mathrm d\theta$ How to calculate:
$$ \int_0^{2\pi} \sqrt{1 - \sin^2 \theta}\;\mathrm d\theta $$

Use Wolfram Alpha!
Plug in "integrate sqrt(1-sin^2(x))". Then press "show steps". You can enter the bounds by hand...
http://www.wolframalpha.com/input/?i=integrate+sqrt%281-sin%5E2%28x%29%29
