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