Solve `l=int_(cos^(4)t)^(-sin^(4)t)(sqrt(f(z))dz)/(sqrt(f(cos 2 t -z))+sqrt(f(z)))`

x = (sin^3t)/(sqrt(cos 2t)), y = (cos^3 t)/(sqrt(cos 2t)) .

int_0^(pi//2)(sqrt(sin x))/(sqrt(sin x) + sqrt(cos x)) dx equals:

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (c) int_(0)^(pi/2)(sqrt(sinx))/(sqrt(sin x) + sqrt(cos x))dx

int(sin x)/(sqrt(4-cos^(2)x))dx=

If x = sqrt((1-t^(2))/(1+t^(2)) and y = (sqrt(1+t^(2))-sqrt(1-t^(2)))/(sqrt(1+t^(2)) + sqrt(1-t^(2))) then (d^(2)y)/(dx^(2)) =

If the number x,y,z are in H.P. , then sqrt(yz)/(sqrt(y)+sqrt(z)),sqrt(xz)/(sqrt(x)+sqrt(z)),sqrt(xy)/(sqrt(x)+sqrt(y)) are in

sin ^(-1)[cot ((sin ^(-1) sqrt((2-sqrt(3))/(4)))+cos ^(-1) (sqrt(12))/(4)+sec ^(-1) sqrt(2))]

int dx/(sqrt(cos^(4)x-cos^(2)x sin^(2)x) ) =