Question

Problem #9: Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 7yzi + 9x j +6yzet k ,S is the portion of the paraboloid z = 36 x? normal on S points away from the z-axis. + for 0 sz s 4, and the unit 64. -3648*pi Enter your answer symbolically, as in these examples Problem #9: -36481 Just Save Submit Problem #9 for Grading Problem #9 Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Your Answer: -40327 -36481 Your Mark: 0/2x 1/2vx Note: Your mark on each question will be the MAXIMUM of your marks on each try. (So there is no harm in making another attempt at a partially correct answer.)

Answer 1

- 3=4 2 2 se ? + paraboloid z - volta 36 64 - 3 = 0 3=4 i boundary came C is = 4 (+) y? X 36 t 64

x= 12 Case y = 18 sino where 3=4 OSOS 2T .. 4 Ciss r(O)= (12 Caso, 16 Sino, O ECO,27] → do=C-12 Sino, 16 cos 0,07 linds (F. dr O=27 F(r(e)).d(ro)) 2T Il [7(16Sino) (4) i +9 (12 Cas@) j +6016 Sino)(4) p2 coscas? *] • (-12 Sino inoit 16 Casoy + ok] do -ZT TE [-5376 Sin?0 +1728 Cas?o] do 5*(-2688 (1-C420) +864C1+Cay 20]do

[-1824 +3552 Ces 20] do - LE** +3552 [18246 +1776 Sinzo]. 20 = -1824(21-0) + 1776 (Sin 4T - Sino) - 36481