Let f(x) = ∫₀^x g(t) log((1 - t)/(1 + t)) dt, where g is a contin… | JEE Main 2024 Mathematics PYQ

NVAMediumJEE Main 2024 · 27 January, Shift 2Properties of Definite Integrals

Let $f(x) = \int_0^x g(t) \log\left(\frac{1 - t}{1 + t}\right) \, dt$ , where $g$ is a continuous odd function. If $\int_{-\pi/2}^{\pi/2} \left(\frac{f(x) x^2 \cos(x)}{1 + e^x}\right) \, dx = \left(\frac{\pi}{\alpha}\right)^2 - \alpha$ , then $\alpha$ is equal to:

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