InterviewSolution
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InterviewSolution
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`int_(pi/3)^(pi/2) sqrt(1+cosx)/(1-cosx)^(5/2) dx`A. `(3)/(64)`B. `-(3)/(64)`C. `(-3)/(64)`D. `-(1)/(128)` |
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Answer» Correct Answer - B ` int _(pi//3) ^(pi//2) (sqrt(1+cos x))/((1-cos x)^(5//2) ) dx ` ` int _(pi//3)^(pi//2) (sqrt(2 )cos. x/2)/(2^(5//2) sin^(5). x/2) dx = 1/4 int _(pi//3)^(pi//2) (cos.x/2)/(sin^(5).x/2)dx` Put `sin. x/2 = t` ` rArr = 1/2 cos. x/2 dx= dt` Also at ` x= pi/3 , t = sin. pi/6 = 1/2 ` and at ` x = pi/2 , t = sin. pi/4 = 1/(sqrt(2))` So integral ` = 1/2 int _(1//2) ^(1//sqrt(2))(dt)/(t^(5) ) = 1/2 [ (-1)/(4t^(4))]_(1//2)^(-1//sqrt(2))` ` = (-1)/8 [ 1/4 - 1/16 ] = (-3)/128` |
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