Question

Use Stokes' Theorem to find SC F. dr where F(x,y,z) = (-y, x,x) and C is the curve of intersection of the plane y = 2 and the paraboloid y + x2 + z2 = 6. Show all work. Please select file(s) Select file(s)

Answer 1

Perlebice orientation litoke's Theorem let o be an oqſented amooth durface that is bounded by a dimple boundary Also led Ê be a F. doo SS anlf. dB ux mesed to exaberete Sfida 1:7629,2) +3,20,30and C: curve interdiction paraboloid + 2 + 2 = 6 a dimples, Cloaded, amoo th curve c with S Fida vector field then of g the plane g = 2 and the At intersection, 24 & ²7 2 = 6 of ² + 2 + 2 = 4 = 2² 2

o gf. Jik ә ду эч 22 a 1. he 02 22 ох, 304 x O ЭХ 92 (а 2) (, к( 9, 1-9 ) oi -j tole ke be 12 --

let s ke on disc x + 2 = 4, y = 2 dels pangsmotuze this oliface as follows d: īU,V) = < U cos(v), 2, US (V)) ds shxon DU OV <Cos), O IN DU o on OV @ elinu) <-U8nCV), o, ulos@)) d ( Х k dince) -us) ở 1 fps(0) 2 du Coscu,o ov i la OXUCOSU) - Ox bine -ox fioke) –j (olestubecasy -Cusino kaimi) +( COSCU Dxo - fu sio (u)) xo) = oi-j(2 cošW) + u gen?@)) +ok - aj also De Fous and

ď s on the plome let D be flee y=2 Z U= 2 OLUL 2 ocv call Semi P de Santiago SSED:Eng) lechu S Saulronter x duch 2 ie Vo U=0 21 2 ndi s uducu W ) du S2 - 0 Jowo 27 2 du 2 (vene 4 T required answer
Thank you.