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AP EAMCET · Maths · Definite Integration

If 01xm(1-x)ndx=k01xn(1-x)mdx, then the value of k equals

  1. A m
  2. B n
  3. C 1mn
  4. D 1
Verified Solution

Answer & Solution

Correct Answer

(D) 1

Step-by-step Solution

Detailed explanation

Given: ∫01 1-xnxmdx=k∫01 xn 1-xmdx ⇒I(m,n)=∫01 xm 1-xndx ⇒∫0a fxdx=∫0afa-xdx ⇒I(m,n)=∫01 1-xm 1-1-xndx ⇒I(m,n)=∫01 1-xm 1-1+xndx…