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COMEDK2017MathematicsDefinite Integration

If _ a ^ b x^ n x^ n +(16-x)^ n d x=6 , then

Options

  1. Aa=4, b=12, n R
  2. Ba=2, b=14, n R
  3. Ca=-4, b=20, n R
  4. Da=2, b=8, n R

Correct answer

B. a=2, b=14, n R

Step-by-step solution

_ a ^ b x^ n x^ n +(16-x)^ n d x=6...(i) Let a+b=16 , then _ a ^ b (16-x)^ n (16-x)^ n +x^ n d x=6..(ii) Adding Eqs. (i) and (ii), we get _ a ^ b 1 d x=12 b-a=12 Solving a+b=16 and b-a=12 , we get a=2, b=14, n R

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