InterviewSolution
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InterviewSolution
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`int_(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)`A. `pi/12`B. `pi/2`C. `pi/6`D. `pi/4` |
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Answer» Correct Answer - A Let `l=int_(pi//6)^(pi//3)(dx)/(1+sqrt(tan x))= int_(pi//6)^(pi//3)((sqrt(cos x))/(sqrt(sin x)+sqrt(cos x)))dx` `rArr l = int_(pi//6)^(pi//3)(sqrt(sin x))/(sqrt(cos x)+sqrt(sin x))dx` ….(ii) `[because int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx]` On adding Eqs. (i) and (ii), we get `2l=int_(pi//6)^(pi//3)1dx=[x]_(pi//6)^(pi//3)=(pi)/(6)` `rArr " " l = (pi)/(12)` |
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