Question

Solve:${\int }_0^{\log 2}\cos 2xdx$=

Answer 1

${\int }_0^{\log 2}\cos 2xdx$

Let $t=\sin 2x\Rightarrow dt=2\cos 2xdx\Rightarrow \cos 2xdx=\frac{dt}{2}$

When $x=0\Rightarrow t=0$

When $x=\log 2\Rightarrow t=\sin 2\log 2$

$={\int }_0^{\sin 2\log 2}\frac{dt}{2}$

$=\frac{1}{2}{\left[t\right]}_0^{\sin 2\log 2}$

$=\frac{1}{2}[\sin 2\log 2-0]$

$=\frac{1}{2}\sin 2\log 2$