Q. $\int_{}^{}{\lbrack f(x)g^{''}(x) - f^{''}(x)g(x)\rbrack}dx$ is equal to
A) $\frac{f(x)}{g^{'}(x)}$
B) $f^{'}(x)g(x) - f(x)g^{'}(x)$
C) $f(x)g^{'}(x) - f^{'}(x)g(x)$
D) $f(x)g^{'}(x) + f^{'}(x)g(x)$
Explanation
(c)
$\int_{}^{}{f(x)g^{''}(x)dx - \int_{}^{}{f^{''}(x)g(x)dx}}$
$= \lbrack f(x)g^{'}(x) - \int_{}^{}{f^{'}(x)g'(x)dx\rbrack - \lbrack g(x)f^{'}(x) - \int_{}^{}{g^{'}(x)f^{'}(x)dx}\rbrack}$
$= f(x)g^{'}(x) - f^{'}(x)g(x)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.