Determining double integral limits

[JasonHathaway]

Homework Statement

Evaluate $\iint\limits_S \vec{A} . \vec{n} ds$ over the plane $x^{2}+y^{2}=16$, where $\vec{A}=z\vec{i}+x\vec{j}-3y^{2}\vec{k}$ and S is a part from the plane and R was projected over xz-plane.

Homework Equations

Surface Integral and Double Integration.

The Attempt at a Solution

This is an answered problem, but I didn't get how to determine the integration limits

I understand that I have to integrate with respect to x and z due the fact the region is projected over "xz-plane", and I've to get the limits from the plane equation.

The limits integration in the solution are $\int_0^5 \int_0^4 dz dx$

 

[LCKurtz]

Homework Statement

Evaluate $\iint\limits_S \vec{A} . \vec{n} ds$ over the plane $x^{2}+y^{2}=16$, where $\vec{A}=z\vec{i}+x\vec{j}-3y^{2}\vec{k}$ and S is a part from the plane and R was projected over xz-plane.

Homework Equations

Surface Integral and Double Integration.

The Attempt at a Solution

This is an answered problem, but I didn't get how to determine the integration limits

I understand that I have to integrate with respect to x and z due the fact the region is projected over "xz-plane", and I've to get the limits from the plane equation.

The limits integration in the solution are $\int_0^5 \int_0^4 dz dx$

$x^2+y^2=16$ is not a plane. It's a circular cylinder standing on the xy plane. And you haven't told us how high it goes in the z direction. Draw a picture to see what its projection on the xz plane would look like.

 

[JasonHathaway]

And that's what confusing me, there's no height. So the problem is wrong, isn't?

 

[haruspex]

I can't make sense of the problem statement. What is R? Is this quoted word for word?