User talk:185.37.110.40

Note: There is potentially a problem with this method. The substitution $$x=r \sin\theta $$ leads to $$dx=r\cos \theta d\theta$$ as stated, but this requires knowing that $$ \frac{d \sin\theta}{d\theta}=\cos\theta $$. This in turn relies on the fact that $$ \lim_{\theta\rightarrow 0}\frac{\sin\theta}{\theta}=1$$. Most elementary proofs of this fact depend on knowing the area of a sector, and in turn the area of a circle - the exact thing that the proof purports to be calculating. So the argument is circular.

This edit was deleted with the comment that it belongs on the talk page. The method it's referring to is the method of finding the area of a circle by integrating the function $$ \sqrt{r^2-x^2} $$ from -r to r. I stand by this comment.