Q. $\int_{- 2}^{2}{e^{\sin^{2}x}\cos^{3}{x\ dx}}$ is equal to
A) $- 1$
B) 0
C) 1
D) $\pi$
Explanation
(b)
Let $I = \int_{0}^{\pi}{e^{\sin^{2}x}\cos^{3}{x\ dx}}$ …(i)
$\Rightarrow \ I = \int_{0}^{\pi}{e^{\sin^{2}{(\pi - x)}}{\cos^{3}(\pi -}{x)\ dx}}$
$\Rightarrow \ I = - \int_{0}^{\pi}{e^{\sin^{2}x}\cos^{3}{x\ dx}}$ …(ii)
On adding Eqs.(i) and (ii), we get
$2I = 0\ \Rightarrow \ I = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.