Q. The value of the integral $\int_{0}^{\frac{\pi}{2}}{(\sin^{100}{x - \cos^{100}{x)dx}}}$ is
A) $\frac{1}{100}$
B) $\frac{100!}{(100)^{100}}$
C) $\frac{\pi}{100}$
D) 0
Explanation
(d)
Let $I = \int_{0}^{\frac{\pi}{2}}{\sin^{100}{xdx - \int_{0}^{\frac{\pi}{2}}{\cos^{100}{xdx}}}}$
$= 0 - 0 = 0$
$= 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.