Question

Prove that the value of the integral, $\int\limits_0^{2a} [f(x)/ f(x) + f(2a-x)] dx$ is equal to a

• A. 162
• B. 132
• C. 21 32
• D. 2123

Answer 1

Answer: (A)

162

Answer 2

Let $I=\int \limits_0^{2a} \frac{f(x)}{ f(x )+f(2a -x )} dx$ .......(i)
$I=\int \limits_0^{2a} \frac{f( 2a-x)}{ f(x )+f(2a -x )} dx$ ........(ii)
On adding Eqs. (i) and (ii), we get
$2I= \int \limits_0^{2a} 1 dx = 2a \Rightarrow I=a$