# Homework Help: Cylindrial Coordinates to evaluate the integral

1. Sep 28, 2016

### nysnacc

1. The problem statement, all variables and given/known data

2. Relevant equations
x^2+y^2 = r^2

3. The attempt at a solution
I think it is asking me to find the volume of the sphere, which is in the first octant (1/8 of the sphere)

So I set
0<= z<= √1-r2
0 <= r <= 1
0<=θ<=π/2

2. Sep 28, 2016

### Ssnow

Hi, remember that if you want the volume of $D$ you must calculate $\int\int\int_{D}1dxdydz$ where $f(x,y,z)=1$ ...

3. Sep 28, 2016

### nysnacc

I think the question wants me to use the du dv

4. Sep 28, 2016

### Ssnow

no because $f(x,y,z)\not=1$ ...

5. Sep 28, 2016

### nysnacc

?

6. Sep 28, 2016

### Ssnow

What I want to say is that your coordinates are ok $x=r\cos{\theta}, y=r\sin{\theta}, z=z$ but evaluating the integral you don't have the volume of the sphere (as you said ...) but simply a result that is the evaluation of the integral ...

7. Sep 28, 2016

### nysnacc

So simply put, do I just plug in the limits:
0<= z<= √1-r2
0 <= r <= 1
0<=θ<=π/2

and into the zex2+y2+z2

then the integral will be something like ∫∫∫∫ z dz r dr dθ

8. Sep 28, 2016

### LCKurtz

Your integrand will be $ze^{x^2+y^2+z^2}$ in cylindrical coordinates with $dV = r~dz~dr~d\theta$.

9. Sep 28, 2016

### nysnacc

Okay but where does z goes (it was before $e^{x^2+y^2+z^2}$)

10. Sep 28, 2016

### LCKurtz

???. Right where I have it.

11. Sep 28, 2016

### nysnacc

I rewrite my thought
Originally I have limits:
0<= z<= √1-r2
0 <= r <= 1
0<=θ<=π/2

Then I use them on ∫ ∫ ∫

replace also ex^2+y^2+z^2 with er2+z2

Then I have ∫ ∫ ∫ z er2+z2 r dz dr dθ