Q. If $\int_{}^{}{f(x)\cos{x\ dx = \frac{1}{2}\left\{ f(x) \right\}^{2} + c,\ then\ f(x)}}$ is
A) $x + c$
B) $\sin{x + c}$
C) $\cos{x + c}$
D) $c$
Explanation
(b)
$\because f(x)\cos{x = \frac{1}{2} \bullet 2f(x)f^{'}(x)}$
Then, $f^{'}(x) = \cos x$
$\therefore f(x) = \sin{x + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.