Q. $\int_{}^{}{\cos^{3}{x.e^{\log{\sin x}}dx}}$ is equal to
A) $- \frac{\sin^{4}x}{4} + c$
B) $- \frac{\cos^{4}x}{4} + c$
C) $\frac{e^{\sin x}}{4} + c$
D) None of these
Explanation
(b)
Let $I = \int_{}^{}{\cos^{3}x}.e^{\log{\sin x}}dx = \int_{}^{}{\cos^{3}x}\sin xdx$
Put $\cos x = t\ \ \ \ \ \ \Rightarrow \ \ \ \ - \sin xdx = dt$
$\therefore\ \ \ \ I = - \int_{}^{}t^{3}dt = - \frac{t^{4}}{4} + c = - \frac{\cos^{4}x}{4} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.