Question

22 + y2 with (1 point) The region W lies between the spheres x2 + y2 + z2 = 1 and 22 + y2 + x2 = 4 and within the cone z = z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of F=ri+y +z3k Out of S. flux =

Answer 1

we have W = {(2,4, 2); x² + y² + 2²-1 and x² + y² + 2² - 4 and within the cone z = √x²+y? ; zzo } and P = x² + y² i + ² Ĉ div ² = 2 (23) + 2 (93) + 2 (23) = 3x² + 3y² + 32² = 3 (x² + y² + ²) rut x = r asosind y= using sind z= rand x² + y² + 2² = r² coire sino + r sine sind + read = er [ (hire + Sinze) sind + Cad] - 12 sind +628] - (1) x² + y² + z = r² =) dw = r² sind drdodo as x² + y² + ² = 1 and x² + y² + z = 4 = 2² i le r²s 2² = 15 452 o ravieso to 27 3 oso<25 as z= Sxty2 a z²= x² + y² is cone with semi-vertical angle / . & racies o to la (1²) (r sind dedodo flan = II J di vê du = 15 [32*+*+22) dv. = 5 I 13(62)(4+ sind) dland do =3 dos sind do 5 est de =3103" come

5 Flux = -3 ( 27-0) (G.Ata - Goo) 2 - 1 ==32(-1 ) x 2 -3 x 2** love u 2-3x3x X=(2-82) x 31 - 2 - 93T (2-2)