Question

Evaluate: ${\int }_0^{\frac{\pi }{4}}\sin 2xdx$

Answer 1

Let $I={\int }_0^{\frac{\pi }{4}}\sin 2xdx$

$=[\frac{-\cos 2x}{2}{]}_0^{\frac{\pi }{4}}$

$=\left[\frac{-\cos 2\left(\frac{\pi }{4}\right)}{2}\right]-\left[\frac{-\cos 2\left(0\right)}{2}\right]$

$=0-\frac{-1}{2}$

$=\frac{1}{2}$

$\therefore {\int }_0^{\frac{\pi }{4}}\sin 2xdx=\frac{1}{2}$