Evaluate the following integrals: ^ 2 _0 1- 2x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\sqrt{1-\cos2\text{x}}\text{ dx}$

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Answer

$\int\limits^{\frac{\pi}{2}}_0\sqrt{1-\cos2\text{x}}\text{ dx}$
$=\int\limits^{\frac{\pi}{2}}_0\sqrt{2\sin^2\text{x}}\text{ dx}$
$=\int\limits^{\frac{\pi}{2}}_0\sqrt{2}\sin\text{x}\text{ dx}$
$=-\sqrt{2}\Big[\cos\text{x}\Big]^{\frac{\pi}{2}}_0$
$=-\big(0-\sqrt{2}\big)$
$=\sqrt{2}$

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