Why does this integral cut off the z component?

[grandpa2390]

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?

 

[BvU]

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]

 

[Ray Vickson]

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.

 

[grandpa2390]

Yes.

thank you :)