# Why does this integral cut off the z component?

• grandpa2390
In summary, the conversation discusses the use of Stoke's theorem to check an example in a textbook. The cross-product of del cross v is calculated and the resulting components are discussed. The direction of da and its notation are also mentioned. Finally, the decision to integrate only the x component is questioned and it is determined that it is because da points in the x direction.
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?

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.

grandpa2390
Ray Vickson said:
Yes.

thank you :)

## 1. Why is the z component often excluded from integrals in science?

The z component is often excluded from integrals in science because it represents the direction of the third dimension in a three-dimensional coordinate system. In many scientific experiments and calculations, the z component is not relevant or necessary to consider.

## 2. How does excluding the z component affect the overall result of an integral?

Excluding the z component from an integral can significantly simplify the calculation since it reduces the problem from three dimensions to two dimensions. This can make the problem more manageable and easier to solve.

## 3. Is it always appropriate to disregard the z component in an integral?

No, it is not always appropriate to disregard the z component in an integral. In some cases, the z component may be essential to the problem and cannot be ignored. It is important to carefully consider the problem and determine if excluding the z component is appropriate.

## 4. Can the z component be included in an integral if needed?

Yes, the z component can be included in an integral if needed. In some cases, the z component may need to be included to accurately represent the problem and obtain an accurate result. It is crucial to carefully consider the problem and determine if the z component should be included.

## 5. Are there any advantages to excluding the z component in an integral?

There are several advantages to excluding the z component in an integral. It can make the calculation simpler, reduce the dimensionality of the problem, and potentially save time and resources. However, it is essential to carefully consider the problem and determine if excluding the z component is appropriate for the specific situation.

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