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MHT CET2012MathematicsDefinite Integration

The value of ₀¹ x² (1-x² )^ 3 / 2 d x is

Options

  1. A1 32
  2. B8
  3. C16
  4. D32

Correct answer

D. 32

Step-by-step solution

Let I= ₀¹ x² (1-x² )^ 3 / 2 d x aligned & (let x= d x= d ) I= ₀^ / 2 ² ( ² )^ 3 / 2 d = ₀^ / 2 ² ⁴ d aligned By Gamma function, I= 2+1 2 4+1 2 2 2+4+2 2 = 3 2 5 2 2 4 = 1 2 1 2 3 2 1 2 1 2 2 3 2 = 3 2 2 2 2 3 2 = 32

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