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Definite Integration question

2004 · Shift 0 · Q87

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PYQ Library
JEE Main
Mathematics
Definite Integration
2004 · Shift 0 · Q87

Definite Integration question

2004 · Shift 0 · Q87

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {xg\left\{ {x\left( {1 - x} \right)} \right\}dx}

and

{I_2} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {g\left\{ {x\left( {1 - x} \right)} \right\}dx} ,

then the value of

{{{I_2}} \over {{I_1}}}

is

A
$1$
B
$-3$
C
$-1$
D
$2$

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