Question

State whether following statement is true or false.

2$\int \sin 2x\cos 3x$ $=\frac{-\cos 5x}{5}+\cos x$

• A. True
• B. False

Answer 1

The correct option is A True

Let $I=2\int \sin 2x\cos 3xdx$

$=\int 2\sin 2x\cos 3xdx$

We know, $2\sin c\cos d=\sin (c+d)+\sin (c-d)$

$I=\int \sin (3x+2x)dx+\int \sin (2x-3x)dx$

$=\int \sin 5x-\int \sin dx$ $\because \sin (-x)=-\sin x$

$=\frac{\cos 5x}{5}+\cos x+c$ $\because \int \sin axdx=\frac{-1}{a}\cos ax+c$

$=-\frac{\cos 5x}{5}+\cos x+c.$

Hence, the answer is true.