# Stoke's Theorem

1. Dec 13, 2009

### Dustinsfl

1. The problem statement, all variables and given/known data
Let C be the triangle from (0,0,0) to (2,0,0) to (0,2,1) to (0,0,0) which lies in th plane z=y/2. If F(x,y,z)=-3y^2i+4zj+6xk, calculate integral of C F dot dr using Stoke's Theorm.

2. Relevant equations
For the curl of F, I obtained -4i-6j+6yk.
For N, I obtained 0i-1/2j+k.
0 greater than equal to X greater than equal to 2.
0 greater than equal to Y greater than equal to 2-x.

3. The attempt at a solution
For F dot N, I obtained 3-6y.
Integrated dydx.
After integration, I obtain -2; however, I believe the answer is 14.
What is going wrong?

2. Dec 13, 2009

### tiny-tim

Hi Dustinsfl!
No, you're only using half the curl formula.

3. Dec 13, 2009

### Dustinsfl

What is the other half then?

4. Dec 13, 2009

### tiny-tim

eg ∂Fz/∂y - ∂Fy/∂z

5. Dec 13, 2009

### Dustinsfl

Here is what I obtained then (0-4)i-(6-0)j+(0--6y)k which simplified to -4i-6j+6yk

6. Dec 13, 2009

### tiny-tim

oops!

Sorry, I'm being daft.

Your curl is correct.

But shouldn't this be 3+6y ? …

7. Dec 13, 2009

### Dustinsfl

Yes that was the problem. I have 14 now, thanks.