Question

If $I=\int ({\sin }^{3}x+{\cos }^{2}x\cdot \sin x)dx,$ then the value of $I$ is
(where $C$ is constant of integration)

• A. $\sin x+C$
• B. $\cot x+C$
• C. $\tan x+C$
• D. $-\cos x+C$

Answer 1

The correct option is D $-\cos x+C$

$I=\int \sin x({\sin }^{2}x+{\cos }^{2}x)dx$

$\Rightarrow I=\int (\sin x\cdot 1)dx=-\cos x+C$