Question

x2 + y2 with z 2 0; its (1 point) The region W lies between the spheres x² + y2 + z2 = 4 and x² + y2 + z = 16 and within the cone z = boundary is the closed surface, S, oriented outward. Find the flux of Ě = x; i+y?1+z2k out of S. flux = 5952pi/20(1-1/sqrt2)

Answer 1

♡ Spheres x² + y2 + Z² = 4 x² + y² + z 2 16 Cone Z with Z1,0 th 3 23 7 + 3 + 2 ^ div lî Ja tu tko z ) . = 3202 + 3y2 + 3 z ² = 3 (x² + y2 + z2) F. Ñ ds flun SS S By Gauss divergence theorem SF. Mas SS div F du E SSS 3 (x²+ y 2 + z²) av let a=ssina coxo, y = s sino sind, z= scopo x² + y² + Z² = 82 and p2 = 16 2 ص = प and Scoxo 2م sinzo Cop 20 tezsin 20 sina) 8 sino S coro Tand 7 - 11/4

limite : P = 2 to P = 4 0 - 0 to o T 14 to & = 21 o 114 4 2T Flux 382 82 sino as ao da 2 84 de 1114 = 31.25" * sin egen 3 [°22" [-core [ 85 74 3 o 5 2 - 6 T √ ] [ 992 5. - 59524 ( 1 - 1 / 2 5
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