Q. The value of $\int_{0}^{12a}{\frac{f(x)}{f(x) + f(12a - x)}dx\ is}$
A) $a$
B) $2a$
C) $3a$
D) $6a$
Explanation
(d)
Let $I = \int_{0}^{12a}{\frac{f(x)}{f(x) + f(12a - x)}dx}$ …(i)
$\Rightarrow I = \int_{0}^{12a}{\frac{f(12a - x)}{f(12a - x) + f(x)}dx}$ ...(ii)
On adding Eqs. (i) and (ii), we get
$2I = \int_{0}^{12a}{1dx = \lbrack x\rbrack_{0}^{12a}}$
$\Rightarrow \ I = 6a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.