Q. $\int_{0}^{1}\frac{x^{2}}{1 + x^{2}}\ dx$ is equal to
A) $\frac{\pi}{4} - 1$
B) $1 - \frac{\pi}{2}$
C) $\frac{\pi}{2} - 1$
D) $1 - \frac{\pi}{4}$
Explanation
(d)
$\int_{0}^{1}\frac{x^{2}}{1 + x^{2}}\ dx = \int_{0}^{1}\frac{{1 + x}^{2}}{1 + x^{2}}\ dx - \int_{0}^{1}\frac{1}{1 + x^{2}}\ dx$
$= \int_{0}^{1}1\ dx - \int_{0}^{1}\frac{1}{1 + x^{2}}\ dx$
$= \lbrack x\rbrack_{0}^{1} - \left\lbrack \tan^{- 1}x \right\rbrack_{0}^{1} = 1 - \frac{\pi}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.