Surface Integral Homework: Evaluate ∫∫σ

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Homework Help Overview

The problem involves evaluating a surface integral ∫∫σ over a surface S, which consists of three parts: S1, a portion of a cylinder; S2, a disk; and S3, a portion of a plane. The context is rooted in surface integrals and vector calculus.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to initiate the problem, questioning whether to perform multiple surface integrals or consider an alternative approach. There is discussion about the applicability of the divergence theorem and what specifically is being integrated over the surface.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and considering various approaches. Some guidance has been offered regarding the potential use of the divergence theorem, contingent on the nature of the integral.

Contextual Notes

Participants are grappling with the specifics of the integral to be evaluated and the conditions under which the divergence theorem may apply. There is a noted lack of clarity regarding the type of integral being addressed.

Baumer8993
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Homework Statement


Evaluate ∫∫σ where S is a surface with sides S1, S2, and S3. S1 is a portion of the cylinder x2+y2 = 1 whose bottom S2 is the disk x2+y2 ≤ 1 and whose top S3 is the portion of the plane z = 1 + x that lies above S2.


Homework Equations


Surface integrals, and vector calculus.


The Attempt at a Solution


I am more stuck with starting this problem. Do I need to do two surface integrals, or something else? I am just completely lost on what to do here...
 
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Baumer8993 said:

Homework Statement


Evaluate ∫∫σ where S is a surface with sides S1, S2, and S3. S1 is a portion of the cylinder x2+y2 = 1 whose bottom S2 is the disk x2+y2 ≤ 1 and whose top S3 is the portion of the plane z = 1 + x that lies above S2.


Homework Equations


Surface integrals, and vector calculus.


The Attempt at a Solution


I am more stuck with starting this problem. Do I need to do two surface integrals, or something else? I am just completely lost on what to do here...

What are you integrating over the surface? You can do it by integrating over the three surfaces and adding them or you might replace the surface integral with a volume integral using the divergence theorem if you just need the total over all three surfaces. Just start doing something.
 
I though I could only use the divergence theorem for flux?
 
Baumer8993 said:
I though I could only use the divergence theorem for flux?

Of course, if it's not a flux integral then you can't use the divergence theorem. That's why I was asking WHAT you are integrating.
 

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