JEE Main202524 Jan 2025Morning ShiftMathematicsDefinite IntegrationActual

IfI (m, n)= ₀^1 x^ m-1 (1-x)^ n-1 d x, m, n 0 , then I(9,14)+I(10,13) is

Options

AI (19,27)
BI (9,1)
CI(1,13)
DI (9,13)

Correct answer

D. I (9,13)

Step-by-step solution

aligned & I ( m , m )= ₀^1 x ^ m -1 (1- x )^ n -1 d x & Let x = ^2 dx =2 ~d & I ( m , n )=2 ₀^ / 2 ( )^ 2 ~m -1 ( )^ 2 n -1 d & I (9,14)+ I (10,13)=2 ₀^ / 2 ( )¹⁷( )²⁷ d & +2 ₀^ / 2 ( )¹⁹( )²⁵ d & =2 ₀^ / 2 ( )¹⁷( )²⁵ d & = I (9,13) aligned

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