Determining double integral limits

  • #1

Homework Statement



Evaluate [itex] \iint\limits_S \vec{A} . \vec{n} ds[/itex] over the plane [itex] x^{2}+y^{2}=16[/itex], where [itex]\vec{A}=z\vec{i}+x\vec{j}-3y^{2}\vec{k} [/itex] 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 [itex] \int_0^5 \int_0^4 dz dx [/itex]
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement



Evaluate [itex] \iint\limits_S \vec{A} . \vec{n} ds[/itex] over the plane [itex] x^{2}+y^{2}=16[/itex], where [itex]\vec{A}=z\vec{i}+x\vec{j}-3y^{2}\vec{k} [/itex] 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 [itex] \int_0^5 \int_0^4 dz dx [/itex]

##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.
 
  • #3
And that's what confusing me, there's no height. So the problem is wrong, isn't?
 
  • #4
haruspex
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I can't make sense of the problem statement. What is R? Is this quoted word for word?
 

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