InterviewSolution
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InterviewSolution
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Let `f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx` and `f(0)=0` then `f(1)` isA. `log_(e)(1+sqrt(2))`B. `log_(e)(1+sqrt(2))-(pi)/(4)`C. `log_(e)(1+sqrt(2))+(pi)/(4)`D. none of these |
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Answer» Correct Answer - b We have , `f(x) = int(x^(2))/((x^(2)+1){1+sqrt(1+x^(2))})dx` `rArrf(x) = int((sqrt(1+x^(2))-1))/((x^(2)+1))dx=int(1)/(sqrt(x^(2)+1))dx=int(1)/(x^(2)+1)dx` `rArrf(x) = log_(e)(x+sqrt(x^(2)+1))-tan^(-1)x+C` Now , `f(0) =0= rArr0=log_(e)1-tan^(-1)0+CrArrC=0` `thereforef(x) =log_(e)(x+sqrt(x^(2)+1))-tan^(-1)x` `rArr f(1)=log_(e)(sqrt(2)+1)-(pi)/(4)` |
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