Question

Help. Cant figure this one out. I keep messing up somewhere. please sent full steps. THANKS IN ADVANCE. I will thumbs up!

13. For the vector field F(x, y, z) = (xy + yºz)i + (y2 + x2 +e+2) 3 + (zz - sin(xy) + y2), compute the divergence of Ě, i.e. compute div = 7. F. Then, using the divergence theorem, compute the surface integral (fux across S) ST. P. 25, where S is the outward- oriented, closed surface composed of the upper hemisphere x2 + y2 + 22 = 4 and the disk in the xy-plane 22 + y2 = 4.

Answer 1

Dolu hom R Divergence thensem :- fix - SSS (hof) dv f (x, y, z) = (x + y²2)i + (y² + x2+ 72 ) ft (x2-Sintaystyle dit - P.I-d(xgt hz) + y + x2 + 3) + 0 (x2- Sin xy + y ) da dy Dz and diut a 9+3y+ + x - (3y+x) S us oriented outwards and enclosed by hemisphere x +y + z ² =4 disk x?ty* = 4. The area inside a un spherical system can be of pea <^ < Also dirt 23 (psin $ Sino)+ esimo ceso So, flux = written as and OSO 220 (3p. Sinop Sino) +esin pcoso sind dedøde -LY (sp®Sm?? sin 8 Sin®+g*i*?coso) de dodep 27 4 (38in87 f030) Sinºp do dop

2019 (-3603 0 +Sino |** Sinzo delle ()

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