# S16-2A - Math 200 Spring 2010 Worksheet#23 Name 52‘...

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Unformatted text preview: Math 200, Spring 2010 Worksheet #23 Name: 52‘} Section 16-2a Scalar Line Integrals 1. Evaluate the line integral L902 ds where Cis the curve given by C : x :12, y = 22‘, 0 s t 51 CFC): (11:21)) oats-j . .c m z < 9t» => “36w! =0H‘ *4? Slﬁfl. wvs'l'e, out ~\$(‘€(+))_‘ 7‘) d ::~7 2%?! all: :: 2W _ ' ~'-' 21'. ‘ 51991 '. (emPu‘lE d5 '4 Ilal‘l'llfdt: ‘ . I. 1 Yx cl = 9 ' L“ : t“ t zwl c Y 4 [Qt 'lll-t‘+\cl'l, ail-CUE“ Qtd’t [du=2'td)‘t. ] a L 1 .. __ 3... '- .. 31.. —'f2(u-ll\51du = 2‘; gyL-uy‘ do. ‘ l [Isa Lg'hyll ' Tg‘ﬁ? l5 2. Evaluate the line integral ILxdswhere C consists of the are C1 of the parabola y =1:2 from (0,0) to (1,1) followed by the line segment C2 from (1,1) to (3,2). Pqume-l'rRI'c C. ‘, '6‘“) =<t 117 Ct. , J c. hm {3N axon : Nth-t" alt =43 (H‘H‘fgfl (513 ‘9 O Pcmme‘l'ﬁk Cz‘. CH)3([4301!)+t<¥2>=<lﬁtl+tz —-l J 4 A _ cm: 42:) z) ndmpﬁ Cut—i “I: ' (W's-s f — ‘ ' r. :nijﬁﬂll? I LIXd-Q ~£0+1ﬁﬁdt ._. “*3 (when: = 26.5 3. (a) Compute thellzlne integlrzal of the scalar function f (x,y,z)=xzz over the curve Cwith parameterization c(t) = <e’,J§t,e—‘), 0 St S 1. C (Ell ‘-'- (et Lr—i ic—t 7 ___> 1 J C.: C, u(,, Him-2’; step: : (Wm do = H'c‘limdt '. nth)" = 51291: were Ou'l Hem}: = cit, 1+8“: glam?) : 28.3 _- LEAVE-t: ft ‘= eﬁ-Pf—t‘ do .3 (€t+e~t)A—t 5&3: Chmpol’ﬂ_ ‘Hua {oi-earn! I 5;¥(x,5}r)da :ﬁﬂa’ﬁwﬂzhmat ale; {euetllf =f(el"*+n)at 2i1t+t)‘_ i2. l L L 2? 0 ' (16“)“1 : zlt’ﬁl t_,-‘l: ‘ _ -| .. )0 ~ e-e -(t~l) = eec‘ “I mm 't -t = ‘ ‘ ojﬁ’ +9 241' of.) cosLttH-t: 2 S'inkﬁ.))5 =23inkﬂ) 26-19 4. Find the mass of the helical spring .1: = 2 cos t, y = t, z = 2 sin t for 0 s t s 6:: , with a density of P(x,y,z)=2y Eff) :- (2 cos—t} t/lsint> I a 5, téé-m Th) = (~21In'tﬂ/2 cos+> ' ME'HHI = : 6‘s : 6"? 1 ‘— L m gffxin-zﬁla : 5 27°14 : 2t.'}§°\,t :.-. J31: I a:J§(6-n)J-:36d§'ﬂ’ c O o 5. Calculate the total the mass of a circular piece of wire of radius 4 cm centered at the origin whose mass densit is x, =x2 cm. \ . . y p( y) g] pummel-radian etc- CirCulqr mm mun V346“ '- — 1 “A '°+‘*‘“‘Wm—J;x 44 eterﬂcostﬁst‘w,ostém CH)= (quantum) :3 m :52“ A “Cm” = “‘*\$"v~*)’*+(mtv -—-. t . a. 2 Heart) - ‘Ht “'5 (if “casti- dt a o : éﬁjm+asg~tit : 1+ 0 Homework #23 _ Reread Section 16.2 (Due 04/21) Do Section 16.2 Exercises: 5, 10, 17, 19, 21 ...
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S16-2A - Math 200 Spring 2010 Worksheet#23 Name 52‘...

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