I was messing around proving the area of a circle using trigonometric substitution. However, I ended up with area = -πr^2. In my integral I ended up using trigonometric substitution and setting x = r*cos(theta) However, this yields x = -r*sin(theta)*d(theta). When that's substituted back into my integral, I ended up with the negative value for area. Why is it that if I were to use a different angle theta and express x = r*sin(theta) that I end up with the correct area? Thanks a lot, as always.