Why does this integral cut off the z component?

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Homework Help Overview

The discussion revolves around an example related to Stokes' theorem, specifically examining the integral of the curl of a vector field and its relation to the differential area element. The original poster is trying to understand why only the x component of the integral is considered in their calculations.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand the reasoning behind focusing on the x component of the integral, questioning whether it is due to the orientation of the area element. Other participants suggest clarifying the notation and terminology used in the context of Stokes' theorem.

Discussion Status

The conversation includes attempts to clarify the notation and the reasoning behind the integral's focus on the x component. Some participants provide brief affirmations regarding the original poster's understanding, but there is no extensive exploration of alternative interpretations or methods.

Contextual Notes

The original poster expresses reluctance to share the full problem statement, indicating a potential constraint on the information available for discussion. There is also a mention of specific nomenclature that may not be universally understood by all participants.

grandpa2390
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Homework Statement


Please don't make me post the entire question. If so, can I take a picture of the example in my textbook?

I am looking at an example in my textbook where we are to check Stoke's theorem

After doing the cross-product of del cross v I get (4z^2-2x)[x hat] + (2z^2)[z hat]
since da points in the x direction
da =dydz[x hat]

Homework Equations



integral of del cross v dot da

The Attempt at a Solution



when they do the integral, it is of the x component alone. why? is it because da is pointing in the x direction?
 
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You could at least divulge what C, S and F are (seehttp://www.math.harvard.edu/archive/21a_spring_09/PDF/13-07-Stokes-thm.pdffor nomenclature) (I suppose your da is his dS ?)

And ##\ \hat x\ ## reads a lot easier than [x hat]
 
grandpa2390 said:

Homework Statement


Please don't make me post the entire question. If so, can I take a picture of the example in my textbook?

I am looking at an example in my textbook where we are to check Stoke's theorem

After doing the cross-product of del cross v I get (4z^2-2x)[x hat] + (2z^2)[z hat]
since da points in the x direction
da =dydz[x hat]

Homework Equations



integral of del cross v dot da

The Attempt at a Solution



when they do the integral, it is of the x component alone. why? is it because da is pointing in the x direction?

Yes.
 
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Likes   Reactions: grandpa2390
Ray Vickson said:
Yes.

thank you :)
 

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