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Question

If A=π0cos x(x+2)2dx,thenπ20sin2x(x+1) dx is equal to
  1. A121π+2
  2. 1π+2A
  3. 1+1π+2A
  4. 12+1π+2A


Solution

The correct option is D 12+1π+2A
A=π0cos x(x+2)2dx=(cos x(1x+2))π0π0(sin x)(1x+2)dx
=1π+2+12π0sin xx+2dx
A=1π+2+122π20sin2x2x+2dx
π20sin2x1+xdx=1π+2+12A

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