Actually either or can be substituted. The whole idea is to make use of the Pythagorean Identity to simplify the integrand to something that can be integrated.
I was looking at the proof of the area of a circle in my book and I understood up to the part y = +/- ((r^{2} - x^{2})^{0.5}) but then the book said to substitue x with rsin(theta).
I understood everything that was done after this but what I dont understand is why rsin(theta) was used instead of rcos(theta). If theta is the angle the radius r makes with the x axis in the 1^{st }quadrant, shouldn't x = rcos(theta)? Can someone explain?
Thanks