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$$\theta$$rsin$$\theta$$z) 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.