Indefinite Integration 1 Question 80
81. Prove that the value of the $\int _0^{2 a}[f(x) /{f(x)+f(2 a-x)}] d x$ is equal to $a$.
integral, $(1988,4$ M)
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Solution:
- Let $I=\int _0^{2 a} \frac{f(x)}{f(x)+f(2 a-x)} d x$
$$ I=\int _0^{2 a} \frac{f(2 a-x)}{f(2 a-x)+f(x)} d x $$
On adding Eqs. (i) and (ii), we get
$$ 2 I=\int _0^{2 a} 1 d x=2 a \Rightarrow I=a $$
