MathematicsThe area between y=tanx and X- axis from x=0 to x=π4

The area between y=tanx and X- axis from x=0 to x=π4

  1. A

    π4

  2. B

    22

  3. C

    log2

  4. D

    log2

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    Solution:

    The given curve is y=tanx

    The rough sketch of the required area is as shown below

     

    The required area is the area of the shaded region.

    The area of the shaded region is the area of the region bounded by the curve y=tanxx=0 and x=π4 with X- axis

    Hence the area of the shaded region is A=0π4tanxdx

    A=0π4tanxdx =logsecx0π4 =log2-log1 =log2

    Therefore, the area of shaded region is log2

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