The value of the integral  ∫0π xsin⁡x1+cos2⁡xdx, is 

The value of the integral  0πxsinx1+cos2xdx, is 

  1. A

    π22

  2. B

    π24

  3. C

    π28

  4. D

    π216

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    Solution:

    Let I=0πxsinx1+cos2xdx

    Then,

     I=0π(πx)sin(πx)1cos2(πx)dx I=0π(πx)sinx1+cos2xdx

    Adding (i) and (ii), we get

    2π=π0πsinx1+cos2xdx2I=π1111+t2dt, where t=cosx2I=πtan1t11=ππ4π4=π22 I=π24

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