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Definite Integration question

2024 · 27 Jan · Shift 2 · Q54

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JEE Main
Mathematics
Definite Integration
2024 · 27 Jan · Shift 2 · Q54

Definite Integration question

2024 · 27 Jan · Shift 2 · Q54

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f(x)=\int\limits_0^x g(t) \log _{\mathrm{e}}\left(\frac{1-\mathrm{t}}{1+\mathrm{t}}\right) \mathrm{dt}

, where

g

is a continuous odd function. If

\int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+\mathrm{e}^x}\right) \mathrm{d} x=\left(\frac{\pi}{\alpha}\right)^2-\alpha

, then

\alpha

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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