Evaluate : `int_(0)^(pi//2) sin^(3) c cos x dx`

Evaluate : int_(0)^(pi//2) sin^(3) x cos x dx

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

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

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

Evaluate :int_(0)^((pi)/(2))(a sin x+b cos x)/(sin((pi)/(4)+x))dx

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

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x) dx . Hence, evaluate int_(0)^(pi//2) (sin x - cos x)/(1+ sin x cos x) dx.

Evaluate: int_(0)^((pi)/(2))2sin x cos x tan^(-1)(sin x)dx

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