Course: Calculus II
Topic: Parametric, Polar, and Conic Curves
Subtopic: Calculus of Polar Curves


Some calculus operations can be simplified by working with equation in polar form rather than rectangular form. All the calculus we have done with rectangular equations we'll redo in this lesson but using polar form. We'll find derivatives and integrals of polar equations, slopes of tangent lines to polar curves, arc lengths of polar curves, and more.


By the end of this topic you should know and be prepared to be tested on:

Terminology & Formulae

Be sure you are able to properly use each of these three formulas with polar equations.

First Derivative of a Polar Equation:  `dy/dx= (r*costheta+(dr)/(d theta)*sintheta)/(-r*sintheta+(dr)/(d theta)*costheta)`

Arc Length of a Polar Curve:  `"AL"= int_alpha^beta sqrt(r^2 + ((dr)/(d theta))^2) d theta` 

Area in a Polar Curve:  `"Area" = 1/2 int_alpha^beta r^2 d theta`

Mini-Lectures and Examples

STUDY: Calculus of Polar Equations

Supplemental Resources (recommended)

Simple sheet with Calculus Formulas for Polar Equations from Dr. Rayman, Univ. of N. Florida.

Supplemental Resources (optional)

Video: Areas and Arc Lengths using Polar Coordinates, Selwyn Hollis's Video Calculus

Lesson: Calculus in the Polar Coordinate System, Dale Hoffman's Contemporary Calculus

rev. 2021-03-06