`int_0^(2pi) sin^2x cos^4x dx`

int_0^pi sin^4x cos^4x 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 5 x cos 4x dx=

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

int_(0)^(pi/2)sin^(2)x cos^(4)x dx=

If int_(0)^(pi//2)sin^(4)x cos^(2)x dx=(pi)/(32) , then int_(0)^(pi//2)sin^(2)x cos^(4)x dx=

(i) int_0^pi (sin^2 x/2- cos^2 x/2) dx (ii) int_0^(pi//2) (sin^2x)/(1+cosx)^2 dx

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

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