Green's theorem- integral over an ellipse

  • Thread starter aylwin
  • Start date
  • #1
1
0

Homework Statement


Use Green's theorem to find the integral ∫C (y^2dx+xdy) when C is the following curve (taken counterclockwise): the ellipse x^2/a^2 + y^2/b^2 =1.


Homework Equations


Green's theorem: ∫C Mdx+Ndy = ∫∫R (∂N/∂x-∂M/∂y)dA


The Attempt at a Solution


I tried parametrizing the ellipse as r(t)=(acost,bsint), but didn't know how to go on...

I don't know how to solve the double integral over the ellipse ∫∫R (1-2y)dA.

Thanks.
 

Answers and Replies

  • #2
557
1
Begin with simpler things to get an idea: how to calculate the area of a circle of r=1?
[tex]\int_{-1}^1\int_{???}^{???} dx dy[/tex]

Replace the ???, then it should be clear for the ellipse.
 

Related Threads on Green's theorem- integral over an ellipse

  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
887
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
1
Views
801
Replies
2
Views
4K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
2
Views
3K
Replies
11
Views
3K
  • Last Post
Replies
9
Views
2K
Replies
5
Views
12K
Top