Double integral using polar coordinates

  • Thread starter Miike012
  • Start date
  • #1
1,011
0
The question is in the paint document

I wanted to know why they integrated from 0 to pi and not from 0 to 2pi
 

Attachments

  • Math.jpg
    Math.jpg
    3.2 KB · Views: 369

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
The question is in the paint document

I wanted to know why they integrated from 0 to pi and not from 0 to 2pi

Draw a picture of the region.
 
  • #3
1,011
0
Draw a picture of the region.

There that is the region I believe
 

Attachments

  • Math 1.png
    Math 1.png
    8.5 KB · Views: 389
  • #4
1,011
0
Sorry I just looked at the question again.. it said above the x-axis
 
  • #5
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
So does that answer your question?
 
  • #6
1,011
0
One last question. When is it best to use polar coordinates rather than spher. coord. For instance if I integrating a cylinder I would use polar and If I was integrating a cone or a ellipsoid I should use spher. coord. But what about elliptical parabaloids or eliptic hyperbolas of one or two sheets?
 
  • #7
1,011
0
To answer my above question (post # 6) I am guessing is depends on my region on the xy plane that I am integrating over..
 
  • #8
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
One last question. When is it best to use polar coordinates rather than spher. coord. For instance if I integrating a cylinder I would use polar and If I was integrating a cone or a ellipsoid I should use spher. coord. But what about elliptical parabaloids or eliptic hyperbolas of one or two sheets?

You have the right general division of the methods. Sometimes they overlap though. A paraboloid would suggest cylindrical coordinates for the elliptical cross section but rectangular if you were doing one of the other cross sections. Similarly for the hyperboloids.
 

Related Threads on Double integral using polar coordinates

Replies
3
Views
3K
Replies
6
Views
1K
Replies
5
Views
8K
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
14
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
12
Views
976
Top