InterviewSolution
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InterviewSolution
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`inttan^(-1)sqrt(x) dx` is equal toA. `(x+1)tan^(-1) sqrt(x) - sqrt(x) + C`B. `x tan^(-1) sqrt(x) - sqrt(x) + C`C. `sqrt(x) - x tan^(-1) sqrt(x) + C`D. `sqrt(x) - (x+1)tan^(-1)sqrt(x) + C` |
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Answer» Correct Answer - A Let ` I = int1.tan^(-1)sqrt(x) dx` `= tan^(-1) sqrt(x). x - 1/2 int (1)/((1+x)). (2)/(sqrt(x))dx` `= x tan^(-1) sqrt(x) - 1/2 int(2)/(sqrt(x)(1+x))dx` Put `x = t^(2) rArr dx = 2t dt` ` :. I = x tan^(-1) sqrt(x) - int (t)/(t(1+t^(2)))dt` `= x tan^(-1) sqrt(x) - int (t^(2))/(1+t^(2)) dt` `= x tan^(-1) sqrt(x) - int (1-(1)/(1+t^(2))) dt` `= x tan^(-1) sqrt(x) - sqrt(x) + tan^(-1) + C` `= x tan^(-1) sqrt(x) - sqrt(x) + tan^(-1) sqrt(x) + C` ` = (x+1) tan^(-1) sqrt(x) - sqrt(x) + C` |
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