Why do I get a negative value if I integrate the parametric curve of a half circle: x(t)=cos(t), y(t)=sin(t), from 0 to pi?
∫y(t)x'(t)dt=∫-cos²(t)dt=-1/2∫1+cos(2t)dt=-1/2(t+sin(2t)/2)+C
At t=pi it is -1/2pi and at t=0 it is 0 so the integral from 0 to pi will be
-1/2pi-0=-1/2pi
Which is what I would expect except it is negative for some reason?