The value of the definite integral ∫a+2πa+5π/2 sin−1⁡(cos⁡x)+cos−1⁡(sin⁡x)dx is equal to

The value of the definite integral a+2πa+5π/2sin1(cosx)+cos1(sinx)dx is equal to

  1. A

    π28

  2. B

    π24

  3. C

    π22

  4. D

    π2

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    Solution:

    sin1(cosx)+cos1(sinx) is periodic with period  2π then

    a+2πa+5π/2sin1(cosx)+cos1(sinx)dx=0π/2sin1(cosx)+cos1(sinx)dx=0π/2sin1cosπ2x+cos1sinπ2xdx=0π/2sin1sinx+cos1cosxdx=20π/2xdx=2x220π2=π24

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