Help for a "Surface and Flux integrals" program

11042017, 09:14 AM
(This post was last modified: 11042017 09:17 AM by salvomic.)
Post: #11




RE: Help for a "Surface and Flux integrals" program
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
Area of a paraboloid with cartesian equation z=x^2+y^2, integrated in a circumference with center in 0,0 and radius 1; we have x=u, y=v, z=u^2+v^2 We want calculate the area of the surface, so the function treated is constant 1. The book suggest \[ \int_{\sigma }1dS=\iint\sqrt{4u^2+4v^2+1}dudv=\int_{0}^{1}\int_{0}^{2\pi }\rho \sqrt{1+4\rho ^2}d \rho d\theta = \frac{\pi }{6} (5^\frac{3}{2}1) \] passing to the polar coordinates... The Prime return another number for the integral (see attached image) and not \( \frac{\pi }{6} (5^\frac{3}{2}1) \) that's about 5.33041350027. Prime return 166.85... So my previous example was so strange to test sfint()... sfint(1,[u,v,u^2+v^2],[0,1],[0,1]) returns another number: 1.861564... Salvo ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

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