If Iₘ,ₙ = ∫₀¹ x^(m−1)(1−x)^(n−1) dx... | Definite Integrals

JEE MAIN 2021

26.02.21_S2

Question

If $I_{m, n}=\int_0^1 x^{m-1}(1-x)^{n-1} d x$, for $m, n \geq 1$ and $\int_0^1 \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} d x=\alpha I_{m, n}, \alpha \in R$, then $\alpha$ equals

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JEE Main

Mathematics

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