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

int_0^(pi/2) sin x dx

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

Evaluate int_0^(pi/2) sin^7x dx

Evaluate : int_(0)^(pi//2) sin x dx

Evaluate: int_0^(3//2) |x sin pi x| dx .

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

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

Evaluate : int _(0)^(pi//4) sin 2x sin 3 x dx

Prove that : int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x)dx hence evaluate : int_(0)^(pi//2) (sin x)/(sin x + cos x) dx