# S 15-2B - Math 200 Spring 2010 Worksheet 24 Name 5 Section 16-2b Vector Line Integrals l The ﬁgure shows a vector ﬁeld F and two curves Cl and

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Unformatted text preview: Math 200, Spring 2010 Worksheet # 24 Name 5?; Section 16-2b Vector Line Integrals l. The ﬁgure shows a vector ﬁeld F and two curves Cl and C2 (3.) Is the line integral L F-ds positive, negative, or zero? Explain. \led’ors jinn-ink; a; C. pole in roungLi-lne fame dimiés 05 CI ,50 +109 i‘Ghaeh'l'ia] COthhen-l— F's-if i5 Pagdﬂe' ' Titus, .2 Ed? = 5‘.” E «in is [Josh‘be . (b) Is the line integral LzF-ds positive, negative, or zero? Explain. No UQc‘l‘or‘S \$‘i'mi: On CL Poid’ {in "HM Scum! d1;‘€c;+t.oh\Q5 C31 while some on. PPOln'l' tin P092”: ﬁeoffosli‘e d‘f‘t’d‘tdn, f So YET)“ =5 F-Td ‘5 nea {ire c A cl 4 I 3 - .,,.__..... ﬂ 2. Evaluate F - ds , where F(x, y,z) : zi + yj — xk and C is the oriented curve parametrized by e(t) = (t,sint,cost) for 0 s t s :r . C’lﬂ': <1) cost) —- 51kt) Hail) 1' <Cast ) SlhtJ“t> H a —: __.r 1’? . . PM '“‘ ; HEM-cant : f<ctrsl§)5mt)"t>'<l)COS—t)"5lnt N1: C. c o .; “ n [A Jnhgtq-‘h-‘Oy pails tut &v:s|'n'l:ah~ - f(cos't +9131 (0le +tsfnt) at did-“1t vz—cas'l: 0 ﬂ. = [sat + £55.34: + (-‘tcost+siht)]o = 4mm = H 3. Evaluate the line integral waag; dx+eydy where C is given by c(t) = (t4,t2) for 0 s t S1 .1, 3 a 9‘“ V - _, a 4 Cu): 32t 4:» Qua, Just 2 Xydx-t'td) -ﬂﬁkﬁpﬁﬁﬁﬂﬂﬂ Gt, > cﬁ: Mu: _. ’ 3 1 I a ‘ “oﬂdl*tl{‘l~t)+et(3t))dt =j('-H;+Jtet)alt 9+ 7 1' 3 D _ _ 1; 3' ’ 7t+€ in 1"- §+e~l = 6-7 4. Evaluate the line integral L y3dx + xzdy where (a) C = Cl is the line segment from (0,1)to (1,0). A 1 dx 43 my" c Permit-52*: C. : can =(t, |~t) ,bﬁ’tii , (Lime-41,4» , It“; sf" ' 2 ' I I. 3 l M vaw‘ay (Pm-l +t‘(-z)at = f(1—3t+1t—t’)at {saunas} J x | (b) C=C2 isthelinesegmentﬁ‘om (1,0)to (0,1). ° = Pg +1 4 __ _ \ ° to,“ C 3 2 [I 1 3 3 H 71 SEN-C. dx+xal 1 a+ a :-« 3 l _#_.1 :1 “In Cly y -C'y x x 7 i174X1-X cl? - (a [2 (C) C= C3 is the arc ofthe parabola x =1—y2 from (0,1) to (1,0), g d d _ (5‘) Nut am. meme: C1,: EH) : (11") t) 1 05¢“ )c(t)=4_3t),> I ﬂz-li’d- ' 3 I 1 I 9:1? c3?“ +>837 = " 272%:le = ‘5-L3(—2tl+(l~t2)- I at =Sft"+;t‘-,)dt ‘4 l _. 2 0 “'°‘ = = ii‘+%’3—t° 1., = 4:1”?! = 1‘3 5. Find the work done by the force ﬁeld F(x, y) = xsin yi+ yj on a particle that moves along the 173arabolay=x2 from (-—1,1) to (2,4). Paramehhe’ gt-eaitltzjl 4: t5 1 (w w, 5? gr, 1 I 671:) =4 1.91:? , " - :: . , 3 (4‘ C C 4 j {tgm‘t £1 2t)clt ‘5 Smit‘hl't )5”: l) _l j J I ‘- "'3 = uteri: +5i‘iq) :— éDS-rms l “fa-‘51 I ,V?kwég§{(Q 6. Find the work done by the force ﬁeld F(x,y)= —y,x) acting onanobject ,/ / .r w as it moves along the parabola y=x2— 1 from (1,0) to (—2,3). 5 " C: 2'." = 7:, __ f _4_. w’fE-olf:.. er 1,") (“C/(“23” 5): -C C‘- a C(+):<l)2.t> C. \ ,1. \ \ .. 1 '1- L "j<l~ilt>‘<112‘h>clt =S( l—‘L' +2'l: )A’C \\" -1. a \3‘. ......... .. -J. = 5 (1+th = t + H}, : *2 =§ - ((+4) = "4 MEI—«\$339? will 13:“ to: 7. Let C: C1 +C2 where C1 is the quarter Circle x +y2 = 4, z: 0, from (0,2,0) to (2,0,0), \$3,003, a): (I:sz where C2 is the line segment from (2,0,0) to (3,3,3). Compute the work done along C by the I a ‘ force F(x,y,z)=(y+z,z—x,x+y+z). A 4 gunmen-:24 AG. 1 at): (29in, my: l, 05“)? I Exit): (ltOStJ‘25|;\-LJO> F (“Em at) = < 22cm, ﬁlsikt, zsgtumst > 62+) : <Hca51t + “#51131; > -'-' ‘1~ Pemw’wiae a; are = (M) < 2,0,o>+t are”, cit-‘4 a, 31mm} 3133'” F (cm "5711 : 25,37 .57” .- 6t+ét~é+31t+£= 331: w: 1".”1j'1E-A iﬂ'd- ‘7; ’ 1L- 33 (rad (é d4+ecF°l4 *0} Ha++f33tdt =21t+ 334(0— 1717*“: 8. The force exerted by an electric charge at the origin on a charged particle at a point (x, y,z) with position vector r = (x, y, z) is F(r) : Kr/HrH3 ,where K is a constant. Find the work done as the particle moves along a straight line from (2,0,0) to (2,1,5) . Assume that F is given in newtons and the unit of distanceisthemeter- at) = (t-t) (2,0,0) + 15 43,55) : (255513 3 oft 1‘! 5... lkcgj: it: ‘15) J ‘5 :4x1919>= <1,t,S’c> ,H?“ = 044%? bur-mez) rs _ , ‘2 30 c ‘ W’ (0259“ - Khmer * Kl 4'2- 30 ° _-_- .1. FE“ ~);.] __ ‘ _i I. l ‘1' q 1 Homework #24 Reread Section 16.2 1 \ Q“ 1, — k[ to 1.] ‘ K[2 —éo] u - Li +3“; . , a = 2 . (Due 04/21) Do Section 16.2 Exerc1ses: 3, 13, 24, 25, 27, 31, 35, 39, 40, 41, 48, 49 lid ‘1 It“; Prepare for next class session: Read Section 16.3 3‘ u‘ " 23‘“; ...
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## This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

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S 15-2B - Math 200 Spring 2010 Worksheet 24 Name 5 Section 16-2b Vector Line Integrals l The ﬁgure shows a vector ﬁeld F and two curves Cl and

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