JEE Main 202126 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002If Im,n=∫01xm−1(1−x)n−1dx{I_{m,n}} = \int\limits_0^1 {{x^{m - 1}}{{(1 - x)}^{n - 1}}dx}Im,n=0∫1xm−1(1−x)n−1dx, for m, n≥1n \ge 1n≥1, and ∫01xm−1+xn−1(1+x)m+1dx=αIm,nα∈R\int\limits_0^1 {{{{x^{m - 1}} + {x^{n - 1}}} \over {{{(1 + x)}^{m + 1}}}}} dx = \alpha {I_{m,n}}\alpha \in R0∫1(1+x)m+1xm−1+xn−1dx=αIm,nα∈R, then α\alphaα equals ___________.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
