Calculating Integral of C F dot dr Using Stoke's Theorem

[Dustinsfl]

Homework Statement

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.

Homework 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.

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?

 

[tiny-tim]

Hi Dustinsfl!

For the curl of F, I obtained -4i-6j+6yk.

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

 

[Dustinsfl]

What is the other half then?

 

[tiny-tim]

eg ∂F_z/∂y - ∂F_y/∂z

 

[Dustinsfl]

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

 

[tiny-tim]

oops!

Sorry, I'm being daft.

Your curl is correct.

But shouldn't this be 3+6y ? …

For F dot N, I obtained 3-6y

 

[Dustinsfl]

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