Q. If $f(x)$ is an odd function and has a period $T$, then $\phi(x) = \int_{0}^{x}{f(t)dt}$ is
A) A periodic function with period $T/2$
B) A periodic function with period $T$
C) Not a periodic function
D) A periodic function with period $T/4$
Explanation
(b)
$\because\ \phi^{'}(x) = f(x)$
$\therefore\ \phi(x)\$is a periodic function with period $T.$ Because $f(x)$ has the period $T$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.