JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

f(x)=\frac{e^x}{1+e^x}, I_1=\int\limits_{{f(-a)}}^{f(a)} x g\{x(1-x)\} d x

and

I_2=\int\limits_{{f(-a)}}^{f(a)} g\{x(1-x)\} d x

, where

g

is not an identity function. Then the value of

I_2 / I_1

, is

View answer and explanation

Correct option: C

Option C (2) is correct because by using the property

\int_a^b f(x) dx = \int_a^b f(a+b-x) dx

, we find that

I_2 = 2I_1

, thus

I_2/I_1 = 2

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