JEE Main & Advanced
Mathematics
Indefinite Integrals
Question Bank
Numerical Value Type Questions - Integrals
question_answer
Let f be a positive function. Let \[{{I}_{1}}=\int\limits_{1-k}^{k}{x\,\,f\left[ x\left( 1-x \right) \right]}\,dx,\] \[{{I}_{2}}=\int\limits_{1-k}^{k}{\,f\left[ x\left( 1-x \right) \right]}\,dx,\] where \[2k-1>0\]. Then \[\frac{{{I}_{1}}}{{{I}_{2}}}\] is