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JEE Main20245 Apr 2024Evening ShiftMathematicsDefinite IntegrationActual

Let ( m , n )= ₀^1 x^ m -1 (1-x)^ n -1 ~d x, ~m , n >0 . If ₀^1 (1-x¹⁰ )²⁰ ~d x= a ( b , c ) , then 100( a + b + c ) equals____

Options

  1. A1021
  2. B2120
  3. C2012
  4. D1120

Correct answer

B. 2120

Step-by-step solution

I= ₀^1 1 (1-x¹⁰ )²⁰ d xx¹⁰=tx=t^ 1 / 10 d x= 1 10 (t)^ -9 / 10 d tI= ₀^1(1-t)²⁰ 1 10 (t)^ -9 / 10 d tI= 1 10 ₀^1 t^ -9 / 10 (1-t)²⁰ d ta= 1 10 b= 1 10 c=21

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