Help for a "Surface and Flux integrals" program

11042017, 10:21 AM
Post: #14




RE: Help for a "Surface and Flux integrals" program
(11042017 09:14 AM)salvomic Wrote: I can't solve this problem; I'm following a book that perhaps report a wrong result: (π/6)*(5^(3/2)1) > 5.33041350027Hi Salvo, You must paramtrise with polar coordinates from the start; the way you are doing it, your are not integrating over a circle in the (x, y)space but a square (your image is missing but that is what I think you are doing) E.g. parametrise the surface as \[ (x=u \cos(v),\ y = u \sin(v),\ z= u^2)\] where \[(u,v) \in [0,1] \times [0,2 \pi] \] and this will make \[ I = (\cos(v), \sin(v), 2 u) \times (u \sin(v), u \cos(v), 0) = (2 u^2 \cos(v),  2 u^2 \sin(v), u) \] and \[ I = \sqrt{4 u^4 + u^2} = u \sqrt{1 + 4 u^2} \] etcetera... 

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