Question

Find an anti derivative (or integral) of the following function by the method of inspection: sin 2x

Answer 1

The anti derivative of sin 2x is a function of x whose derivative is sin 2x. It is known that,

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

$\Rightarrow$ sin 2x = -$\frac{1}{2}\frac{d}{dx}$(cos2x)

∴ sin 2x = $\frac{d}{dx}\bigg(-\frac{1}{2}cos2x\bigg)$

Therefore, the anti derivative of sin 2x is -$\frac{1}{2}$ cos 2x