InterviewSolution
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InterviewSolution
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The value of `int_(1)^(2) (dx)/(x(1+x^(4))` isA. `(1)/(4)log.(17)/(32)`B. `(1)/(4)log.(32)/(17)`C. `log.(17)/(2)`D. `(1)/(4)log.(17)/(2)` |
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Answer» Correct Answer - B Let ` l = int_(1)^(2) (dx)/(x(1+x^(4)) ) =int_(1)^(2) (x^(3))/(x^(4) (1+x^(4)))dx` Put ` x^(4) = t rArr 4x^(3) dx = dt` ` :. l = 1/4 int_(1)^(16)(dt)/(t(1+t))= 1/4 int_(1)^(16) (1/t - 1/(1+t))dt` ` = 1/4 (log. t/(1+t))_(1)^(16) = 1/4 (log. 16/17 - log. 1/2 )` ` = 1/4 log. 32/17 ` |
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