`int sin ((n pi x)/2)dx`

If x in(-pi,pi) then int sqrt(1+sin((x)/(2)))dx

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

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

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

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

If quad A_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sin x)dx;B_(n)=int_(0)^((pi)/(2))((sin nx)/(sin x))^(2)dx; for n in N, then

int_(-pi/2)^( pi/2)(dx)/([x]+[sin x]+4)

int_0^pi (x sin x)/(1+sin x) dx=pi/2 (pi-2)