Flux Integral for a Surface Above a Disc with Downward Orientation

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Homework Help Overview

The problem involves computing the flux of a vector field through a specified surface. The vector field is given as F = xi + yj + zk, and the surface S is defined as the part of the paraboloid z = x^2 + y^2 that lies above the disc defined by x^2 + y^2 ≤ 4, with a downward orientation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the limits of integration, particularly questioning why the integrand extends to 4 when the radius of the disc is only 2. Some express confusion over the solution guide's information.

Discussion Status

The discussion is currently addressing discrepancies between the original poster's understanding and the information provided in the solution guide. Some participants have reached out to their teacher for clarification, indicating that there may have been an error in the online homework.

Contextual Notes

There is an ongoing examination of the assumptions regarding the limits of integration and the radius of the disc, with references to external resources such as solution guides and teacher feedback.

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QUESTION: Compute the flux of the vector field, F , through the surface, S.

F = xi+yj+zk

S is the part of the surface z = x^2 + y^2 above the disc x^2 + y^2 ≤ 4 , oriented downward.

I am just wondering why the integrand is from o to 4 while the radius is only 2.

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It isn't. That's incorrect. It should be 2.
 
My solution guide says otherwise, along with my online homework
 
HallsofIvy said:
It isn't. That's incorrect. It should be 2.

I just emailed my teacher and he said there was an error in the online homework. The correct answer is indeed used with radius 2. Sorry about that.
 

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