Q. If $\int_{}^{}{f(x)dx = f(x) + c,\ then\ \int_{}^{}{\left( f(x) \right)^{2}dx}}$ is
A) $\left( f(x) \right)^{2} + k$
B) $\frac{1}{3}\left( f(x) \right)^{3} + k$
C) $f(x) + k$
D) $\frac{1}{2}\left( f(x) \right)^{2} + k$
Explanation
(a)
Given, $\int_{}^{}{f(x)dx = f(x) + c}$
$\Rightarrow f(x) = f^{'}(x)$
$\therefore\ \int_{}^{}{(f(x)^{2})dx = \int_{}^{}{f(x) \bullet f^{'}(x)dx}}$
$= \frac{1}{2}\left( f(x) \right)^{2} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.