- #1

- 15

- 0

## Homework Statement

Verfify Stokes' theorem for the given surface S and boundary ∂S, and vector fields F.

S = [(x,y,z): x

^{2}+y

^{2}+z

^{2}=1, z≥0

∂S = [(x,y): x

^{2}+y

^{2}=1

F=<x,y,z>

I did this problem and checked the answer - I chose the wrong integral bounds and I am wondering why they are wrong.

## Homework Equations

Stokes' theorem:

∫∫(∇×F)dS = ∫F⋅ds

## The Attempt at a Solution

I was able to do the left hand of the solution easily. I knew that I should get zero for the cross product, so that's all I had to do.

For the right hand side:

∫F⋅dS = ∫xdx+ydy

x= cosΘ

y=sinΘ

dx=-sinΘ

dy=cosΘ

0≤Θ≤2π

Apparently this is the correct range for theta:

0≤θ≤π

Why is it just π?