Help for a "Surface and Flux integrals" program

[AlexFekken]

(11-04-2017 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) -> 5.33041350027

Hi 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...