Homework Help: Double integral using polar coordinates

1. Nov 9, 2012

Miike012

The question is in the paint document

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

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2. Nov 9, 2012

LCKurtz

Draw a picture of the region.

3. Nov 9, 2012

Miike012

There that is the region I believe

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4. Nov 9, 2012

Miike012

Sorry I just looked at the question again.. it said above the x-axis

5. Nov 9, 2012

6. Nov 9, 2012

Miike012

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. Nov 9, 2012

Miike012

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. Nov 9, 2012

LCKurtz

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.