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 XY-Plane | Applications of Integration

The length of arc in rectangular coordinates is given by the following formulas:

$\displaystyle s = \int_{x_1}^{x_2} \sqrt{1 + \left( \dfrac{dy}{dx} \right)^2} \, dx$   and   $\displaystyle s = \int_{y_1}^{y_2} \sqrt{1 + \left(\dfrac{dx}{dy} \right)^2} \, dy$

 

length-of-arc-xy-plane.jpg

 

See the derivations here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-xy-plane-...
 

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