Prove that `I =int_(0)^(pi//2)(sqrt(secx))/(sqrt("cosec"x)+sqrt(secx))dx =pi/4`

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

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

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

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

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

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

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

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

Prove that, int_(2)^(3)(sqrt(x)dx)/(sqrt(x)+sqrt(5-x))=(1)/(2)

Prove that 2sin(pi/8)=sqrt(2-sqrt2)