Areas and Lengths Using Polar Coordinates

Sick of ads?‚Äč Sign up for MathVids Premium
Taught by Houston
  • Currently 3.0/5 Stars.
6406 views | 4 ratings
Meets NCTM Standards:
Lesson Summary:

In this lesson on areas and lengths using polar coordinates, students learn how to compute the area of a region in which R is between 0 and F of theta and theta is between angles alpha and beta, and how to find the length of a polar arc where r equals alpha theta for theta between alpha and beta. The lesson also includes examples such as finding the area inside a cardioid and the area between polar curves. Students are taught how to compute the perimeter of the cardioid, and they also learn how to find the length of the curve of r equals theta for theta between zero and two pi.

Lesson Description:

Area of a polar region; length of a polar arc.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

Questions answered by this video:
  • How do you find areas using polar coordinates?
  • How do you find arc length using polar coordinates?
  • How do you find the area inside r = 1 + cos theta?
  • What is the area inside r = sin (3theta)?
  • How do you find the area between two polar curves?
  • How do you find the area between r = 2cos theta and r = 1?
  • How do you find the area between r = sin(3theta) and r = sin theta?
  • What is the equation for length of a polar arc?
  • How do you find the perimeter of r = 1 + cos theta?
  • How do you find the length of the curve r = theta between 0 and 2pi?
  • Staff Review

    • Currently 4.0/5 Stars.
    This lesson is really interesting. You will learn to find area and arc length using polar coordinates, which can be much easier in many instances. Many examples are shown. This is a really helpful lesson if you are trying to understand how to find area and arc length using polar coordinates.