Double integral using polar coordinates

[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

 

[LCKurtz]

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.

 

[Miike012]

Draw a picture of the region.

There that is the region I believe

 

[Miike012]

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

 

[LCKurtz]

So does that answer your question?

 

[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?

 

[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..

 

[LCKurtz]

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.