`int_0^(pi/4) sinx /cos^2 x dx`

Evaluate (i) int_0^(pi//4) sin x cos x dx (ii) int_0^(pi//2) (1 + cos x)^(1//2) dx (iii) int_0^(pi//2) (1 + sin x)^(1//2) dx (iv) int_0^(pi//4) (1 -cos 2x)^(1//2)dx

int_0^pi sin^4x cos^4x dx

int_0^(pi/2) (sinx)/(1+Cos^2x)dx

If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx. then

int_0^(pi//2) x^2 cos 2x dx

Evaluate int_0^(pi/2) x/(sinx+cosx)dx

(i) int_0^(pi/2) sin^2 x dx (ii) int_0^(pi//2) cos^2 x dx

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