InterviewSolution
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InterviewSolution
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` int_(-1)^(1)log(x+sqrt(x^(2)+1))` dx is equal to |
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Answer» Correct Answer - A Let f(x) = log `(x+sqrt(1+x^(2)))`and replacing x by -x , we get ` f(-x) = log (sqrt(1+x^(2))-x)` ` = log [ (sqrt(1+x^(2))-x) ((sqrt(1+x^(2))+x))/((sqrt(1+x^(2))+x))]` ` = log. ([ (1+x^(2))-x^(2)])/((sqrt(1+x^(2))+x))= log 1 - log (sqrt(1+x^(2))+x)` ` = - log (sqrt(1+x^(2))+x)=f(x)` Hence, f(x) is an odd function . ` :. int _(-1)^(1) log (x+sqrt(1+x^(2)))dx = 0 ` |
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