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Question

Evaluate the definite integral π40tanxdx

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Solution

Let I=π40tanxdx

tanxdx=log|cosx|=F(x)

By second fundamental theorem of calculus, we obtain

I=F(π4)F(0)

=log|cosπ4|+log|cos0|

=log12+log|1|

=log(2)12=12log2

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