InterviewSolution
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InterviewSolution
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` int_(0)^(1) (dx)/(e^(x) +e^(-x)) dx ` is equal toA. `pi//4`B. `tan^(-1)e-(pi)/(4)`C. `tan^(-1)e`D. `(pi)/(4)tan^(-1)e` |
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Answer» Correct Answer - B Let ` int _(0)^(1) (dx)/(e^(x)+e^(-x))=int _(0)^(1) (e^(x))/(e^(2x)+1) dx` Put ` t = e^(x) ` ` rArr dt = e^(x) dx` Also at `x = 0 , t = e^(0) = 1 ` at ` x = 1, t = e^(1) = e` ` l = int _(1)^(e) (dt)/(t^(2)+1) = [ tan ^(-1) t] _(1)^(e)` ` tan ^(-1) e - tan ^(-1) (1)` ` = tan ^(-1) e - pi/4` |
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