Parametric equations, polar coordinates, and vector-valued functions

This course is a part of Integral Calculus, a 5-course Topic series from Khan Academy.

We are used to working with functions whose output is a single variable, and whose graph is defined with Cartesian, i.e., (x,y) coordinates. But there can be other functions! For example, vector-valued functions can have two variables or more as outputs! Polar functions are graphed using polar coordinates, i.e., they take an angle as an input and output a radius! Learn about these functions and how we apply the concept of the integral on them.

This course contains 6 segments:

Arc length: parametric curves

Planar motion

Area: polar regions (single curve)

Area: polar regions (two curves)

Arc length: polar curves

You may already be familiar with finding arc length of graphs that are defined in terms of rectangular coordinates. We'll now extend our knowledge of arc length to include polar graphs.

Calculator-active practice