Let f(x)= e^ x 1+e^ x I_ 1 = _ f (- a ) ^ f ( a ) x g(x(1-x)) d x I_ 2 = _ f (- a ) ^ f (…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Let \(f(x)=\frac{e^{x}}{1+e^{x}}\)
\(I_{1}=\int_{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\mathrm{a})} x g(x(1-x)) d x\)
\(I_{2}=\int_{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\mathrm{a})} g(x(1-x)) d x\)
then \(\mathrm{I}_{2} / \mathrm{I}_{1}\) is
\(I_{1}=\int_{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\mathrm{a})} x g(x(1-x)) d x\)
\(I_{2}=\int_{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\mathrm{a})} g(x(1-x)) d x\)
then \(\mathrm{I}_{2} / \mathrm{I}_{1}\) is
- \(1\)
- \(-3\)
- \(-1\)
- \(2\)
Answer
(D) 2
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