polar coordinates

The Polar Coordinate System

In Polar Coordinate System, the references are a fixed point and a fixed line. The fixed point is called the pole and the fixed line is called the polar axis. The location of a point is expressed according to its distance from the pole and its angle from the polar axis. The distance is denoted by r and the angle by θ.

polar-ccordinates.gif

 

Length of Arc in Polar Plane | Applications of Integration

The length of arc on polar plane is given by the formula:

$\displaystyle s = \int_{\theta_1}^{\theta_2} \sqrt{r^2 + \left( \dfrac{dr}{d\theta} \right)^2} ~ d\theta$

 

length-of-arc-polar-plane.jpg

 

The formula above is derived in two ways. See it here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-polar-pla...

Plane Areas in Polar Coordinates | Applications of Integration

The fundamental equation for finding the area enclosed by a curve whose equation is in polar coordinates is...
 

$\displaystyle A = \frac{1}{2}{\int_{\theta_1}^{\theta_2}} r^2 \, d\theta$

 

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