Q. If $\int_{0}^{a}{f(2a - x)dx = m\ }and\ \int_{0}^{a}{f(x)}\ dx = n,$ then $\int_{0}^{2a}{f(x)}dx$is equal to
A) $2m + n$
B) $m + 2n$
C) $m - n$
D) $m + n$
Explanation
(d)
$\because\int_{0}^{2a}{f(x)dx = \int_{0}^{a}{\left\{ f(2a - x) + f(x) \right\} dx}}$
$= \int_{0}^{a}{f(2a - x)dx + \int_{0}^{a}{f(x)dx}}$
$= m + n$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.