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