Question

S 6 Calculate the fleux SSF. ds, where I la, y, z)= <0? 2², 227 and S is the finite cylinder (with top and bottom) given by x² + y² = 1, 2 = 0, Z = 3,

Answer 1

> X Q5 we have = < x, y2, 2²> div² = 2 (1²) + 2 (42) + 3 (22) 2x + 2y +22 2(x+y+z) the finite top and bottom) given by x² + y² = 1 ; 2=0 ; 2=3 Out dir and s is cylinder (with Y = rsino Z = z x = r Coso x² + y2 = r² cośret i sinto r²(costot Sinto) r² (1) x² + y² = r² rardo da dadyd z = za! =! raries raries to as O to 27 as z raries as 0 to 3 flux = Sids' S ss s dire av (by gauss divergence theorem ) V 11 SSS 263+4 + 2) dacdydz -a s fracoso + s (or coso + r sino +z) ode dodz 1 da so coso do sei der + J dz s sinodo faz de z dz s do ser des 0

- + Flur a [ 1 (un ), + ting 2) 곧 13 xol x !!] [ 13-0 Sin2x - Sin) C IS + [3-ol-lenam-ro)) () 호 + X (22-0) X 을 + xx] 11 3 x (0) × 글 + 3 - Cl-1)) 글 [。+o+ 14 존 Flun 29 Flun 2 95 (2)