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If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f...

If `f(x) =(e^x)/(1+e^x), I_1=int_(f(-a))^(f(a)) xg(x(1-x))dx`, and `I_2=int_(f(-a))^(f(a)) g(x(1-x))dx,` then the value of `(I_2)/(I_1)` is

A

`-1`

B

`-2`

C

`2`

D

`1`

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( \frac{I_2}{I_1} \) where: - \( I_1 = \int_{f(-a)}^{f(a)} x g(x(1-x)) \, dx \) - \( I_2 = \int_{f(-a)}^{f(a)} g(x(1-x)) \, dx \) We start by analyzing the function \( f(x) \): 1. **Calculate \( f(a) \)**: ...
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