If f(x)=∫x2+sin2⁡x1+x2sec2⁡xdx and f(0)=0, then f(1) equals:

If f(x)=x2+sin2x1+x2sec2xdx and f(0)=0, then f(1) equals:

  1. A

    tan1π4

  2. B

    π4

  3. C

    tan1+π4

  4. D

    tan1+1

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    Solution:

    We have,

    f(x)=x2+1-1sin2x1+x2sec2xdx f(x)=sec2x-11+x2dx f(x)=tanx-tan1x+C f(0)=0C=0

    Hence, f(x)=tanx-tan1x

     f(1)=tan1-π4

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