Spherical coordinates: x= psin øcoso, y = psin osin 0, z = pcosø so p’ = x² + y2 +z?. SIS F(x, y, z)dv = 7 = La S L f(ps

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Spherical Coordinates X Psin Ocoso Y Psin Osin 0 Z Pcoso So P X Y2 Z Sis F X Y Z Dv 7 La S L F Ps 1 (54.96 KiB) Viewed 24 times

Spherical coordinates: x= psin øcoso, y = psin osin 0, z = pcosø so p’ = x² + y2 +z?. SIS F(x, y, z)dv = 7 = La S L f(psin pcos , psin øsin 0, p cosø) p’ sin odpdodo -0, da Flux integrals: For a continuous vector field F defined on an oriented surface S parametrized by r(u,v), SfF.ds=ſſF(r, xr,)dA (if rı, xr, gives the orientation.) In the special case of a surface z = g(x, y): ſſF.ds = ſſF.(-85, -8,, 1)dA (for an upward normal.) ,} D = S D 1. Find (directly) the surface integral of f(x, y, z)= e over the surface x' + y² = 4,05755.