# Confusion in Stoke's theorem!

1. Dec 19, 2008

### physstudent1

1. The problem statement, all variables and given/known data

Hello, this isn't a specific problem but a part I am confused about in Stoke's theorem. In my text the section on Line integrals (if C(t) is the parameterization of the curve) as the integral of F(C(t))*C'(t) but for vector fields the formula becomes the integral of F(C(t))*||C'(T)|| now I understand this but when I got to Stoke's theorem it says The line integral of the boundary of a surface is equal to the surface integral of the curl vector. However In every example I have seen in my text the F is a vector field so I figured that the line integral should be defined as the integral of F(C(t))*||C'(T)|| but it is the integral of F(C(t))*C'(t) can anyone clear this up for me please if you don't understand my question please ask I will try to reword it more clearly! Thanks!

2. Relevant equations

3. The attempt at a solution

2. Dec 19, 2008

### Defennder

Ok so this is for general line integrals of vector functions.

This is the formula for line integrals of scalar fields, not vector fields.

As above.

3. Dec 20, 2008

### physstudent1

thanks a lot for clearing this up

one more thing, just exactly how could I tell the differnece between a scalar function and a vector function?

4. Dec 20, 2008

### Defennder

Eg.
A scalar function of 3 variables gives you a single (scalar) value $$f(x,y,z) = x + y + z$$ for every point (x,y,z).

A vector function of 3 variables gives you a vector: $$\mathbf{F}(x,y,z) = x \mathbf{i} + y\mathbf{j} + z\mathbf{k}$$ for every point (x,y,z)

5. Dec 20, 2008

### physstudent1

oh that makes sense thanks the other definitions I found online I couldn't really understand but this clears it up well.