[Okta Webinar] Learn how to a build a cloud-first strategyRegister Now

x
  • Status: Solved
  • Priority: Medium
  • Security: Public
  • Views: 2335
  • Last Modified:

limits of integration in polar coordinates

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.
0
maimran
Asked:
maimran
  • 2
1 Solution
 
GwynforWebCommented:
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.

               
0
 
maimranAuthor Commented:
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.
0
 
GwynforWebCommented:
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.

 
0

Featured Post

What does it mean to be "Always On"?

Is your cloud always on? With an Always On cloud you won't have to worry about downtime for maintenance or software application code updates, ensuring that your bottom line isn't affected.

  • 2
Tackle projects and never again get stuck behind a technical roadblock.
Join Now