int_(0)^((pi)/(2))(sin x)/(sqrt(1+cos x))dx

If int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=In2, then the value of int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to:

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

Show that : int_(0)^((pi)/(2))(sin^(2)x)/(sin x+cos x)dx=(1)/(sqrt(2))log(sqrt(2)+1)

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sqrt(sin x))/(sqrt(sin x)+sqrt(cos x))dx

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

Evaluate :int_(0)^((pi)/(2))sqrt(1+sin x)dx

int_(0)^((pi)/(2))(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx

int_(0)^((pi)/(2))(cos^(2)x)/(sin x+cos x)dx=(1)/(sqrt(2))(log(sqrt(2)+1))

Prove that int_(0)^((pi)/(2))(sin^(2)x)/(1+sin x cos x)dx=(pi)/(3sqrt(3))