Prove that : int(0)^(pi//2) (sqrt(tanx))...

Prove that : `int_(0)^(pi//2) (sqrt(tanx))/(sqrt(tanx +sqrt(cotx)))dx=(pi)/(4)`

Answer

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int_(0)^(pi//2)(sqrt(sinx))/((sqrt(sinx)+sqrt(cosx)))dx=(pi)/(4)

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Knowledge Check

int_(0)^(pi//3) [sqrt(3)tanx]dx=

A

`(5pi)/(6)`

B

`(5pi)/(6)-tan^(-1)((2)/(sqrt(2)))`

C

`(pi)/(2)-tan^(-1)((2)/(sqrt(2)))`

D

none of these

int_(0)^(pi//2)((pi)/(4)-x)/(sqrt(sin x)+ sqrt(cos x))dx=

A

`(pi sqrt(2))/(4)`

B

`(pi)/(4 sqrt(2))`

C

0

D

`(pi)/(4)`

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int_(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))\ dx

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int_(0)^(pi//2)(dx)/(1+tanx) is

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