(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let: [tex]\vec{F}(x,y,z) = (2z^{2},6x,0),[/tex] and S be the square: [tex]0\leq x\leq1, 0\leq y\leq1, z=1. [/tex]

a) Evaluate the surface integral (directly):

[tex]\int\int_{S}(curl \vec{F})\cdot\vec{n} dA[/tex]

b) Apply Stokes' Theorem and determine the integral by evaluating the corresponding contour integral.

2. Relevant equations

[tex]\int\int_{S}(curl \vec{F})\cdot\vec{n} dA = \oint_{C}\vec{F}\cdot d\vec{r}[/tex]

3. The attempt at a solution

a) Basically I took the curl of F and got (0, 4z, 6) and dotted it with the normal vector which is either (0,0,+1) or (0,0,-1) as no orientation was given in the question! which gave me a value of +6 or -6.

b) now this is the part which has confused me!! How on earth do I find the corresponding contour integral?? I have no idea how to find dr and I'm not sure what to do about parametizing the square.

Any help would be greatly appreciated!!!

P.S. I have a similar problem involving Gauss' Law so am hoping to kill two birds with one stone!

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# Problem with stokes' theorem

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