_ ^ 2x 3x ;dx = - Vidyadip

MCQ

$\int_{}^{} {\sin 2x\cos 3x\;dx = } $

A
$\frac{1}{2}\left( {\cos x + \frac{1}{5}\cos 5x} \right) + c$
✓
$\frac{1}{2}\left( {\cos x - \frac{1}{5}\cos 5x} \right) + c$
C
$\cos x + \frac{1}{5}\cos 5x + c$
D
$\cos x - \frac{1}{5}\cos 5x + c$

✓

Answer

Correct option: B.

$\frac{1}{2}\left( {\cos x - \frac{1}{5}\cos 5x} \right) + c$

b
(b)$\int_{}^{} {\sin 2x\,\cos 3x\,dx} = \frac{1}{2}\int_{}^{} {2(\sin 2x\cos 3x)\,dx} $
$ = \frac{1}{2}\int_{}^{} {(\sin 5x - \sin x)\,dx} = \frac{1}{2}\left[ { - \frac{{\cos 5x}}{5} + \cos x} \right] + c$
$ = \frac{1}{2}\left[ {\cos x - \frac{{\cos 5x}}{5}} \right] + c.$

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