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Question

Let F(x)=esin1x(1x1x2)dx,andF(0)=1,ifF(12)=k3ex6π, then k = 
  1. π4
  2. π6
  3. π2
  4. π3


Solution

The correct option is C π2
F(x)=esin1x(1x1x2)dx=esin1x(11x21x2x1x2)dxF(x)=esin1x1x2+cF(0)=1+cc=0(F(0)=1)F(12)=eπ6.32=k3πeπ6k=π2

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