1. ∫0^π sin⁡〖x/2〗 cos⁡〖x/2〗 dx

8. ∫0^π {sin^2 (x/2)− cos^2 (x/2)}dx

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

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

int_(0)^(pi) x sin x. cos^(2) 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

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

2int_ (0) | sin x-sqrt (3) cos 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)

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