Troublesome Stokes Theorem Problem

[jegues]

Homework Statement

See figure attached for problem statement

Homework Equations

The Attempt at a Solution

See figure attached for my attempt.

I found this problem to be a little long and drawn out, which leads me to believe I made a mistake somewhere. Is this the case? Or does it just turn this way? Was there an easier way to solve this problem?

Thanks again!

 

[LCKurtz]

Homework Statement

See figure attached for problem statement

Homework Equations

The Attempt at a Solution

See figure attached for my attempt.

I found this problem to be a little long and drawn out, which leads me to believe I made a mistake somewhere. Is this the case? Or does it just turn this way? Was there an easier way to solve this problem?

Thanks again!

That is exactly the way to do the problem, but you did make a mistake. Check your sign on the z component of curl F. But where did you get that integrand for I? It should be curl F dot k which isn't 12xy + 6y². That mistake caused all the extra work (think of it as good practice )

 

[jegues]

That is exactly the way to do the problem, but you did make a mistake. Check your sign on the z component of curl F. But where did you get that integrand for I? It should be curl F dot k which isn't 12xy + 6y². That mistake caused all the extra work (think of it as good practice )

Ah! Good catch!

Thanks, I'll give me the problem another go and see how things unfold.

 

[jegues]

I found another mistake, in the circle in the xy plane, the radius is $$\sqrt{2}$$ not $$\sqrt{3}$$.

I found the final answer to be $$=-12\pi$$

 

[vela]

Just out of curiosity, how did you come up with your original integrand from the curl of F?