- #1
Double integral using polar coordinates
- Thread starter Miike012
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Homework Help Overview
The discussion revolves around the use of double integrals in polar coordinates, specifically addressing the limits of integration and the choice of coordinate systems based on the geometric shape of the region being integrated over.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Participants explore the reasoning behind integrating from 0 to pi instead of 0 to 2pi, with suggestions to visualize the region involved. Questions arise regarding the appropriate use of polar versus spherical coordinates based on the shapes being integrated, such as cylinders, cones, and paraboloids.
Discussion Status
Participants are actively questioning the assumptions related to the integration limits and the choice of coordinate systems. Some guidance has been offered regarding the general applicability of different coordinate systems based on the geometric context, but no consensus has been reached on specific cases.
Contextual Notes
There is mention of constraints such as the integration being limited to the area above the x-axis and the need for visual representation of the region to clarify the integration limits.
- #2
LCKurtz
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Miike012 said:
Draw a picture of the region.
- #3
- #4
Miike012
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Sorry I just looked at the question again.. it said above the x-axis
- #5
LCKurtz
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So does that answer your question?
- #6
Miike012
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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
Miike012
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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
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Miike012 said:
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.
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