# Math Help - Can someone please explain this integration problem to me?

1. ## Can someone please explain this integration problem to me?

I was looking at the proof of the area of a circle in my book and I understood up to the part y = +/- ((r2 - x2)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 1st quadrant, shouldn't x = rcos(theta)? Can someone explain?
Thanks

2. ## Re: Can someone please explain this integration problem to me?

Actually either \displaystyle \begin{align*} x = r\sin{(\theta)} \end{align*} or \displaystyle \begin{align*} x = r\cos{(\theta)} \end{align*} can be substituted. The whole idea is to make use of the Pythagorean Identity to simplify the integrand to something that can be integrated.