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

Evaluate [tex]\int\int Curl F\cdot dS[/tex] where [tex]F=<z,x,y>[/tex] (NOTE: the vector in my post preview is showing me the wrong one despite me trying to correct it, the right one is F=<z,x,y>) and S is the surface [tex] z=2-\sqrt{x^2 +y^2}[/tex] above z=0.

2. Relevant equations

I used Stokes' Theorem, choosing to evaluate [tex]\int_C F\cdot dr[/tex] and using [tex]r(t)=<2cos(t),2sin(t),0>[/tex] as the parametric form of my Curve and after differentiating and dotting with the composed form of F and r, I got 4Pi as my answer after evaluating [tex]\int_0^{2\pi} 4cos^2(t) dt[/tex]

Did I do this correctly? Did I get the right answer? I need to know because as part of this extra credit assignment, I must do this same integral but by not using Stokes Theorem, and before I venture into trying to use the formulas for Flux, I want to know if I got the right answer first.

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# Homework Help: Did I do this right? (Stokes' Theorem, Flux)

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