∫ 4 sin x cos (x/2) cos (3 x/2) d x equals :

Question

∫ 4 sin x cos (x/2) cos (3 x/2) d x equals : (A)  cos x-(1/2) cos 2 x+(1/3) cos 3 x+c (B)  cos x-(1/2) cos 2 x-(1/3) cos 3 x+c (C)  cos x+(1/2) cos 2 x+(1/3) cos 3 x+c (D)  cos x+(1/2) cos 2 x-(1/3) cos 3 x+c

Tardigrade Admin · Accepted Answer

Correct answer is (b) cos x-(1/2) cos 2 x-(1/3) cos 3 x+c

Q. $\int 4 sin x cos \frac{x}{2} cos \frac{3 x}{2} d x$ equals :

$cos x - \frac{1}{2} cos 2 x + \frac{1}{3} cos 3 x + c$

$cos x - \frac{1}{2} cos 2 x - \frac{1}{3} cos 3 x + c$

$cos x + \frac{1}{2} cos 2 x + \frac{1}{3} cos 3 x + c$

$cos x + \frac{1}{2} cos 2 x - \frac{1}{3} cos 3 x + c$

Correct answer is (b) $cos x - \frac{1}{2} cos 2 x - \frac{1}{3} cos 3 x + c$

Q. ∫4sinxcos2x​cos23x​dx equals :

cosx−21​cos2x+31​cos3x+c

cosx−21​cos2x−31​cos3x+c

cosx+21​cos2x+31​cos3x+c

cosx+21​cos2x−31​cos3x+c