If f(x) = (eˣ)/(1 + eˣ),I₁ = ∫ f(- a) ^(f(a)) xg x(1 - x) and I₂ = ∫ f(- a) ^(f(a)) g x(1 - x), then the value of I₂/I₁ is

Integral Calculus: JEE Main 2004 Mathematics question

JEE Main 2004 · Annual, Paper 1 · Q3336

JEE Main 2004Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

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}}}

JEE Main 2004 Integral Calculus Question with Solution (Annual Paper 1, Q3336) | JEE Arc

JEE Main 2004 · Annual, Paper 1 · Q3336

JEE Main 2004Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

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}}}