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int(0)^(pi//2)sqrt(1+sinx)dx...

`int_(0)^(pi//2)sqrt(1+sinx)dx`

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Prove the following : 1 lt int_(0)^(pi//2)sqrt(sinx)dx lt sqrt(pi/2)

int_(0)^(pi)sqrt(1+sinx)dx

int_(0)^((pi)/(2))(sqrt(sinx)dx)/(sqrt(sinx)+sqrtcosx)

int_(0)^(pi//2)(sqrt(sinx)cosx)^(3)dx=?

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

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

Using properties of definite integrals, evaluate int_(0)^(pi//2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

int_0^(pi/2) cosx/sqrt(1+sinx)dx