Question

Find an anti derivative (or integral) of the following function by the method of inspection.

sin 2x

Answer 1

We know that,

${\displaystyle \frac{d}{dx}}$ cos 2x = - 2 sin 2x

or sin 2x = ${\displaystyle -\frac{1}{2}\frac{d}{dx}}$ cos 2x

∴ sin 2x = ${\displaystyle \frac{\text{d}}{\text{dx}}(-\frac{1}{2}\cos 2x)}$

Therefore, the antiderivative of sin 2x is ${\displaystyle -\frac{1}{2}}$ cos 2x.