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Definite Integration question

2021 · 26 Feb · Shift 2 · Q45
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  5. /2021 · 26 Feb · Shift 2 · Q45

Definite Integration question

2021 · 26 Feb · Shift 2 · Q45

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1
If 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∫1​xm−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−1​dx=αIm,n​α∈R, then α\alphaα equals ‾\underline{\hspace{2cm}}​.
Numerical answer
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