`int_0^(pi) sin^2 x/(1+cos x) dx`

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

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

Prove that int_0^a f(x)dx=int_0^af(a-x)dx , hence evaluate int_0^pi(x sin x)/(1+cos^2 x)dx

Evaluate the following integral: int_0^(pi//2)(sin^2x)/((1+cos x)^2)dx

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

The value of int_(0)^(2pi)[sin2x(1+cos3x)] dx, where [t] denotes

The value of int_(0)^(2pi)[sin 2x(1+cos 3x)]dx , where [t] denotes the greatest integer function, is:

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