Q. If $\int_{}^{}{uv''}dx = uv^{'} - vu^{'} + a$, then $a$ is equal to
A) $\int_{}^{}{u''}v\ dx$
B) $\int_{}^{}{u'}v\ dx$
C) $\int_{}^{}{uv'}dx$
D) $\int_{}^{}{u''}\ dx$
Explanation
(a)
Now, $\int_{}^{}{uv''}\ dx = uv^{'} - \int_{}^{}{u'v'}\ dx$
$= uv^{'} - \left\lbrack vu^{'} - \int_{}^{}{vu''}\ dx \right\rbrack = uv^{'} - vu^{'} + \int_{}^{}{u^{''}v}\ dx$
$\therefore\ a = \int_{}^{}{u''}v\ dx$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.