`int_(-pi//4)^(pi//4) sin^(2) x dx`

Evaluate int_(-pi//3)^(pi//3) sin^(3) xdx

Evaluate int_(-pi//2)^(pi//2) ( sin theta cos theta) d theta .

Evaluate int_(0)^(pi//4) sin 2x dx

Evaluate int_(0)^(pi//2) (sin^(3//2)x)/(sin^(3//2)x+ cos^(3//2) 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 - cos x)/(1+ sin x cos x) dx.

Evaluate sin^2(pi/4)+sin^2 (3pi/4)+sin^2(5pi/4)+sin^2(7pi/4)

Prove any of the following: sin^2(pi/4)+sin^2(3pi/4)+sin^2(5pi/4)+sin^2(7pi/4)=2