limits of integration in polar coordinates

Posted on 2003-11-15
Last Modified: 2008-02-01
How to find the limit of integration for an ellipse defined as :
It helps me if you use a detail here plus some use of mathcad or Advanced Grapher or some othersoftware

C: The ellipse 4x^2 + y^2 = 4 in xy-plane, counter clockwise when viewed from the above.
Question by:maimran
  • 2
LVL 31

Expert Comment

ID: 9757624
In polar coordinates 4x²  + y²  = 4    then using  dividing by 4 gives

         x²  + y²/4  = 1

ie      x²  + (y/2)²  = 1

    x=cos(theta) ,   y=2sin (theta)

satisfies the relationship and is the polar coordinate reprentation of the ellipse, and the ellipse is traced out by varing theta from 0 to 2Pi, I do not understand what you mean by the rest of the question.


Author Comment

ID: 9757889
OK, I put the whole question here now.

This is from CAlculus and Analytic Geometery by Thomas Fenny 9th edition( page 1122 )

Use the surface integral in Stoke's Theorem to calculate the circulation of the field F around the curve C in the indicated direction.

  F = x^2 i + 2x j + z^2 k
  C: The ellipse 4x^2 + y^2 = 4 in xy-plane, counter clockwise when viewed from the above.

In the solution manual it just use the result as  ( I quote from the solution )
the last line is
= 2(Area of the ellispe ) = 4 PI
it means he use the area as 2 PI but how, I want this.
LVL 31

Accepted Solution

GwynforWeb earned 100 total points
ID: 9759213
The ellipse is

x=cos(s) ,   y=2sin (s)     ,  0 <= s <= 2Pi

As a vector function this becomes

(x(s),y(s)) = (cos(s), 2sin (s)),  0 <= s <= 2Pi

now apply the theorem with the limits 0 to 2Pi and the result comes out quickly. I am sure you can do the rest.


Featured Post

Does Powershell have you tied up in knots?

Managing Active Directory does not always have to be complicated.  If you are spending more time trying instead of doing, then it's time to look at something else. For nearly 20 years, AD admins around the world have used one tool for day-to-day AD management: Hyena. Discover why

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
which japanese 7-seater is a hybrid like Toyota Prius 26 139
wordsWithoutList  challenge 24 125
Revenue table 8 101
Simplify expression 3 100
This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

831 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question