question_answer

If \[f\left( x \right)=\frac{{{e}^{x}}}{1+{{e}^{x}}},{{I}_{1}}=\int\limits_{f\left( -a \right)}^{f\left( a \right)}{xg\left( x\left( 1-x \right) \right)\,dx}\] and \[{{I}_{2}}=\int\limits_{f\left( -a \right)}^{f\left( a \right)}{g\,\,\left( x\left( 1-x \right) \right)\,\,dx,}\] then find the value of \[\frac{{{I}_{2}}}{{{I}_{1}}}.\]

Answer:

2.00