Convert to cylindrical coordinates

[caliguy]

Evaluate by changing to cylindrical coordinates

\int from 0 to 1 \int from 0 to (1-y^2)^1/2 \int from (x^2+y^2) to (x^2+y^2)^1/2 (xyz) dzdxdy

I came to an answer of integral from 0 to pi integral from 0 to 1 integral from r^2 to r (rcos\thetarsin\thetaz) r dzdrd\theta
Is this the correct answer?

 

[LCKurtz]

Hello Caliguy. Click on the expression below to see how to post it so it is readable in tex:

\int_0^1 \int_0^{\sqrt{1-y^2}}\int_{x^2+y^2}^{\sqrt{x^2+y^2}}xyz\ dzdxdy

This looks like a first octant integral. Check your \theta limits.

 

[caliguy]

To me they seem right, doesn't theta go from zero to pi? after graphing it it looks like a half a circle... maybe I'm overlooking something?

 

[LCKurtz]

Neither x nor y get negative in your original integrals.

 

[caliguy]

So theta only goes from 0 to pi/2 right?

 

[LCKurtz]

So theta only goes from 0 to pi/2 right?

Yes.