Help Rectangle to Cylindrical coordinate question

[tnutty]

Homework Statement

evaluate : $$\int\int\int_{E} e^z DV$$

where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5


I just need help setting this up.

I know that theta is between 0 and 2pi

Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5).

Would the iterated integral set up in cylindrical coordinate look like this :
$$\int^{2\pi}_{0}$$$$\int^{\sqrt{5}}_{0}$$$$\int^{1+r}_{0}e^z dz* r*dr *d\theta$$

 

[HallsofIvy]

Almost. Since the paraboloid is given by $z= 1+ x^2+ y^2$, the limit on z should be $1+ r^2$ not 1+ r.

But have you copied the problem correctly? One of the surfaces bounding the region you give as "$x^2+ r^2= 5$". Was that supposed to be $x^2+ y^2= 5$? If so the two surfaces do NOT completely bound a region. In your integrals you seem to be assuming that the lower boundary is z= 0. Is that given?

 

[tnutty]

>>but have you copied the problem correctly? One of the surfaces bounding the region you give as x^2 + r^2 = 5.

I'm sorry its was real late, its supposed to be x^2 + y^2 = 5.

>>In your integrals you seem to be assuming that the lower boundary is z= 0. Is that given?

No, I wasn't sure so I assumed that part. It does not specify

 

[HallsofIvy]

If that is correct then there is NO region enclosed by those surfaces!