Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
 

Example 4 :

Find the area of a circle of radius $R$.

Solution :
Take the origin to be at the centre of the circle and the plane of the circle to be the $\rho -\theta$plane. Since the area element in the polar coordinates is $\rho d\theta dr$, the area of the circle is

\begin{displaymath}\int_0^{2\pi}d\theta\int_0^R\rho d\rho = 2\pi\left[\frac{\rho^2}{2}\right]_0^R= \pi R^2\end{displaymath}

a very well known result !

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