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Question: Answered & Verified by Expert
∫01x(1−x)3/2dx is
MathematicsDefinite IntegrationKCETKCET 2010
Options:
  • A −235
  • B 435
  • C 2435
  • D −835
Solution:
1311 Upvotes Verified Answer
The correct answer is: 435
∫01x(1−x)3/2dx
=∫01x(2−1)(1−x)5/2−1dx
=B(2,5/2){∵B(m,n)=∫01xm−1(1−x)n−1dx∵B(m,n)=ΓmΓnΓ(m+n)
=Γ2Γ5/2Γ(2+5/2)
=1⋅3/2⋅1/2Γ1/2Γ9/2(∵Γ1/2=π)
=3/4⋅π7/2⋅5/2⋅3/2⋅1/2π=435

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