Calculus Third Editon By Strauss, Bradley and Smith sec7.2,7.3

# Calculus (3rd Edition)

This preview shows pages 1–12. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 3'2. fntqgratfon by Parts 7.2 Iangrntion by Paris. Pagan 439-411 1. 2. = -%rc‘“+%[u_h d2: = ‘EIT-E — -:-c'2'+ 0 [mm —:c.os:+ Jcmzd: = —:wsx+sin=+6 junm = %a3|nx — 'E'Illdl‘u =1r2|I1x—%LR+C [sin-1m =xain_’r—I M“ 31—13 =rnin_1x+Vl—-r2+C [an-am: = —z=cm+ajmm= : —12cna r-I-‘J{.I:ain a: - Jainrd'x) = —:.3coa:+2::ain:+2coar+0 Page 31.? 7. I= Ie‘hmdrdx 1. ll 2—3'sin 42+ ﬁle-3‘ sin 41: d: =%e_3‘ain II: — ﬁgs—s‘m‘h] - ﬁjc‘a‘cw 4: d: §I=§c'3'sin4r — ﬁe'azmséz+ Cl I=ﬁc-3'sin 4: — %e_um54:+ C a. I= [era-mam —§c"m 3:: + H‘sch 3:: dz: Je’rm a: + gym“ 3: 41.2%“: 3:.- dz] I1 = 432.: 3: + yam ﬁx— 3H :91 1,34: -.}¢"m 32+ gehaiu sz+ C1 = -1?§ez‘ms 3r+135ehain Ez-i- C n. Imam: =§¢'ln:-§[=’dz=§ﬂuz _ \$9“: 10. It: +,sin gin: [(23+2nin z+ain“=) dz =§23+Elxsinxdr+ Iain“: dz =H+2isin :— xcoaﬂ+{§_ﬂin42rj + c = g + k+2ﬁnt-2rmru%sin2: + C 11. 3} Jr: “man :3 '— [maﬁa 3:} a: = “inﬁll I) - mﬂn r] — Iaiuﬂn I] d: Page 313 Chapter .7. Mcthod's of Integration 2jsinan r) or: = 451an x: — mun =}1+ 6. = [mun 1'} dz = asinﬂn :) — cosﬂn 2]] + C = In it: 12. [main mmrdrz lilsain 2:: If: =1'Iu2 + C i =5-[—%zcoa2r~J.—'§msﬁrdr] =éluw]”+C _ I I l - _ —ix cm 2r+ :6 am 2.!) + C :%1n2(51n I] + C =—i~rcos‘2:+}l{sin2x+c ‘t 17 Iﬁlnrd: uzlnndv=ﬁd 13. [Inﬁll-F I} d: u: In“:2 +1}; dbl: If: 1 4 ‘1 4. 2 12 2:2 =22‘3'llnz'iI —3§J.::'"r d: =\$lll(l-'2+lj— F—dz 1 +1 _16 43124_32 _2a _ — In 4 — —z _ In 2 I a 1: 1 T "g" = £1.1qu +1) — 2K1 - f) a: ' + 1 Calculator value: 1.282413 2 —1 =x1n{:2+1]-2:+2t.am I+C 13- [Phlsz "=lnndﬂ:x3d 1 e . 2 _ '— 14- [atnﬁdz = if“. 3‘: _ ﬁx: a, 1 :J-ainuﬂwdw] =icq_1lgx4|:=1:n4_%ggq+ﬁ = zjwsm w w ﬂag + 1) : 2{—- mam w+ [can :1: dun] Calculator value: 16.29965 8 2 =2[_wmsw+sin wl+c 19. Jﬂlnx} d: u lnr: u r 1 c :_?’ Imﬂﬁ-l—hinﬁ'lc : mﬂlnzjzlf-Zflnrdz 1 u=||1::;tl=d. c = a|[|n a}? _ 21:11:: I": - [dz] _ 1 =c-%¢lnc-llnl-rlf]=e—-2 Calculator value: {1.71823 8 an. 12.0mm: lan 1: 13:: 3|! = (law: 8 l Section 312. integration by Part: Page 319 3n = t[lnt)2F:—2I1ntdt [MED—dds t:ln.a:;dt=.r_1d. l = Imam ‘3 =a1m6i+lcoﬂtdi=-teost+aini+c = 31201133]: — tin 1P1“ # Id: 1 = —]n .tcoaﬂn r] +sin(1n z) + C _ 2 _ _ e ' sea“ 3 +1} Eiacﬁn 3c} 1?1.] 25. I[ﬁn2:h(m:]]dx:[2 sin rmaxlulﬁeoa 1) d1: = semis. + 21.13“) r2[35{ln3+1]-3e+1] ‘=‘°°“i'=‘“'“ =a=m=a+3h2 =_2[unm Calculator value: 15.913733 1 = —{;Fln1—iltdi] ;= J 2m ‘1' ,1 = —t’ln Hit” + G =‘5e2‘sin ital: —- Jehain 2.1: cl: = arenas: — [meat] ln(eoa 2:) + C E! 25. Ié‘ﬁne‘&:=j¢'sine’[e‘dx) — 24: 1T , [-1,2xm,lg+[etm2m] = [want I " =—1mt+lmtdt:—ieoat+aint+ﬂ : iﬂtﬁi-ir(1)(ﬂ)+%c“(1]4i(lltll — r I 1 =-t"ma:‘+aine"+c _ ESI' 2f— EC — E 27. [[ﬁnxh(2+m:]] dz: — Jim I ﬁt I w 22. Jriainx-lvwar} dz :1 = a: tie: (sin x+eoa :] u = —llnt+£+C = —[2+cna z}lu(2+coa z} + [2 +1105 2:] -+- C 11:31.11“: rd: :3 25" i?—1d‘ ?—1 saw — “tittie— mt- : as?" - i] Calculator value: 133.62291 :r :ayf—cusa:+ain 3H —J(—cos :+aia:} d: a =1r+(ai|tr+eoa tug: :- - 2 Calculator value; 1.11159 :3. Integration by parts is the application of the formula. = ,3}:an - ll -—'EJ1111::2 - 1|(2: dz] l””“"' i”“ =t£luiE-1l—§{E—1)Inir’—1l The H factor is a part of the integrand that is + a? — l) + Cl differentiated and tin in the part that is _ integrated. Generally. pick ﬁle as complicated — tux-i=9 - 1L+ :2} + c as pouaible yet still. integrable, so that the :3 integral on the right is easier to integrate b. cl: = ID: + :(122 - 1.] ’1] d: than the original integral. Chapter 3'. Methods of Integration Page 320 #1 1 _ 1“” _ :“+‘ _ 3.3+:E11'IIEFII‘I'C —mln= =%(lnl:1 — 1I+32I+C 34. Let ﬁt) he the distance traveled. 29. ape”: df= 1r”? 1": -_.I | 1__, n. 0 I 1:. 53 Flu H. = sin 1:03 z+Jisinzx #1: I1 I In: R I. .2. W + b: "——'| G 1 II I DO .k H. 1 -T. u I .:h. n I n. 1-. n + C} =sin zoos x+ Iﬂ —ma=r]d: :sin .rcus 3+ :— [mash = -2e—'”(2 +1] + c 21=ain zmar+ 1+ 6' I 35. - Let (ﬁll) be the number of units produced. _ #3.“ I _ laﬂﬂte I=%{x+ain=coax]+c it? :I" E du=dqu=i+gﬂa£ﬁ¢umhIm29 =-lﬂﬂl}e_‘l‘5+liﬂﬂnslTTunits 35. Let (2U!) be the amount of money raised in t —_- + 5112:] __ + 311142;) a "Rh- £Q_ FUJI =1§+%xsin2:—&§+%m2:+c W‘2;Dﬂmc = 31:! + w“ 2” imam a can) [zoom :1: D : 2,nun{—5tc"”-“] l: + 10,000 I I: “ma =[—1u.uuotc‘°-“ J 50.0%?”‘2’H: x3 if: I: :12. I 11::2 in: I: du:2zdz,u=y‘?+l[roumblﬂnlﬂ = 409.0%" + 50,000 a: \$13,212 VF+1vI2IV9+1£= 2 ar- v=2wj=r=n viii-l El 2 _:2 .1 33. [mm W "(‘" “3*? “J Section 12% fntegratr'an by Part: Page 321 2 21(1 — 3:: ‘2] 5:: 3.73213 41. The curves intersect when .1: = I]. Assume the up: density is 1. 1 3-8- V=21J zﬂainz+cmsaﬂdt A=J(c,_e_,}dz a u . . W"- = 2111-5203: + ran-13+ smx+ «Ist a =2rrw'i — I] x 2.6026 33:; {c' F c")[a‘+¢“}dz c 39. a. VzurJIUnﬂgd: e = nﬂn ﬁll: — EIlen ’3 1'33“ 2 1 I: My: [gif— e‘") d: : {1:{In — 27r(:]n .1: — rjlll a d = (i = — _ =1rl:e-'2¢+25—-2) 5‘ x; u a a] = «(a -— 2] #5 2.2555 =:(e'+a_']|;- [(cr-l-c—‘jd: c I: __ U _ 1 = —- g: _ h. V=21rlzlntdz=21r[5:-[2lnr—ml: HE +c I) I: '3 AIM-J ' {Sue Problem 3] =% a 0.7353 _ e2 1 _Ir 2 _ mtg-+3] -§(e +1) r: 13.1715 cm) W n: (0.63. 1.27] an. The curves intersect when a: = :rrfvi; assume the dcnsiLy '13 1. £1: _ ,_, _ “1' m ‘3‘ 33-“ “:1 . . I'M A = [{coa x—sm this: {smat+cnazjl n J'B-’ I" = Ire—W.” a = 2 — l 5': H.414? mm M =J%(coex-sina:][cosz+sinr)d'r U ‘:ﬂ' "‘1 d w" Iy—uj dy: zuzlnxdz =% cos 22d: = %sin2s:| D = i— = [1.25 era a ff! My:[z{coax-3inz] d: u u=gdu=(coar—ninr]d 2y‘f1=§zmln=—gz3”+c inf-I 1.11:2 ['21 _ I C : :{sint+cus£}|ﬁ:- I {siux-lnmag) d; 29 51:3 (11 .1: 5] + a m 44- £=Itan"a1noley:>o =33! 2 — (-casl:+ain:]| u [9—1 dy=Itau_1xdx =§ 2 —1 a 0.1107 In y=a~um":: — 1§ln(x2+1}+ C _ ﬂrlll]? 0.25 (E, y} a: m. ‘3 [0.27. 0-50) : rta or )! Formuia. 457 Page 322 _£ _I|.12 Atlil,1]. 0—4 T+C _.1 _E Inn y: ﬂan-11: -%1n{272+1:|+%|l12 —% y = exp[rtan_1:—%Ill[z2+l}+%ln2 — {L d9 ﬂy 45+ -Jy" dy: Inward: By parts or - Fol-mu a. 312 -ln|yt=cuaz+rsinz+0 Atﬂﬂ.1).0=l+c,eoﬂ= —1. —|qu1=wer+:einx —l y=exp{1—- one: — xﬁin 3} 1r dli. + f"(::}] Bin 1: d: “(1') sin a: If: IJ ‘31' 11' = sinxdz+ If I] I] 1r = —eos zﬂrjlz-l— If'l’g) cos: dz 0 +sinrf'ﬁx} q: — [ﬁx] ward: a = —cm 11‘ + cos 01(0) This is 0, so that = —fl:|]] = —3. 47, um = —r1nw—;—ﬂ— gt aft} = In“) d1: — £922 + l‘l‘. Since em) = 1] [the rocket. stem at ground level}, we find (by substituting the give information), {120] _ smuoymme- 200:12]]In(3u.M0—m[12n]) — T W. -1§{:«:2}(120)2 + 5.000(120} # 343.33511 9.: \$5 miles Chapter 3', Methods offntegration sun—5]. 43. ——r1-—1[ mlagler som— —m' 3'5 "1—12 :5 TENS db 4!]. Average displacement is: arfs +1 2.3.: ' 0351015 5: e: 3 o E. e_ “51 41.25 cos 5: + 5 sin 51) (— {3.25) + (5} a: 0.0? 50. Let r be the distance from the camera to truck. Then 6 : ten-1(ﬂr_]] — tan—1(e'1] The average value in 20 mﬁ-Ilm' 1w") Aerie-‘11 a: 4 a: HANS-15 (by calculator} The average value of ﬂ is approximately I1. IQVI 51. int cWok: ljnRTln V “3 ' my 1?: luvl 3 :-.. “NJ (In v J In mm “1 V I 133* parts or y Form“ a 499 101? 1%.an V— V— Vln v11| ‘ 1 V 1 = H-‘glﬁﬂin 10 — 9} fl es 1.553nET 52. Section 12. fnrggratr'on by Parts 53. [Her dz 1: = 5 5 . I": rhu = e‘ (If = zne’ — "Jr" _ 12" Jr -'1. [Ell] I)" d: H- : [In 1]"; 1h: = dz; = rﬂn at)" — :aJ.l_']I1r}“'"'d'r 11',” r: I sin“: 4h; n is even: '3 545- 1: : [ﬁin z)“_ I; (h! = sin I . ﬂ H2 = -:;|n" IEHHII N2 + I {u - L}[:niu 2:)” “gnu-121' If: u w: = I] + (u - [:1]. [{sin z}“_2{l - ail|2r1]dr U I,” = [n — l}J‘ Lain 1'}"_1 uh: — [n - I}! U 17;“: "I = [H — HI {sin min—"5 rh- U Tr,” I: H—‘I [sianN "1 rt; 0 This rcuursiw I'nrlnuln will In: with! ritlillilhﬁlly wiLlI 'Ili'LlllL'ﬁ. ul' H lel. IIUL'J'L‘ilhI: I9} '3. rm r=u+“—ﬁ—1[5m“ fun- LI _n—1r5irL“‘3rcmr I”: _ T a 1']? 1'1— lu—J n—I: +--F[—"_2'[sm 1d: 0 1T}: _(ﬂ-{II-Ii] ‘ N_4. _W 5m Li: I: 1: 1 if” _ _ 1-1—1 Lr;-3]-~Ll\$ . _ _. SHIEI dz: PJSEJPS II (1m [Ii-IMH—SH-HJL _ q _ ' WJ{1+LEH-IJ¢E1 I] _ I':I-5-...{“_:§:Il:"_l]-£ If"! For I can”: dx‘ proceed as :ihown. album. [I 1112 I: J :03“: Jr, n is UIIIJ I] u — | ' I” = CH” 1' 5|” J--| U I}: -|— J [H - l]{:'.:m ﬂ" - “Hing:- (If U 1'er U + (u. — IJJ [{cna r}“_ 1“ —r.nH21-.-]] Jr.- u If? = {n - HI {LL35 u:j"_1rh:—(u— [H II If? H! = {u —- [lil‘ {:er J:]"_": rl'J'.‘ u w: I: -—": II {cmsmff'ﬂ2 d: U 'I'llin. munrqiw: I'urInLIL'n will In: Ilhtﬂl rupueuLcully with values 0|" H Um! ttliiH'IJI'I-‘rl: hr 3. if]! I=U+j—"_l|"[ ain't-ltd: ﬂ _ !h— I can" '32: em 2] m " r1 -— 2 u w: + n _ 1 ms”_ 1: r11 D Inf? : cos" _‘lz' «11 .. "(u—'2} ‘ u an“? n {II-lli'i-33'-'[2} :...._ "(Hanan-(3} [coszdz' ll Page 324 I Chapter 3'. Methods of Integrativ- _2*4'ﬂ""iﬂ—3l["—1} __t 3 15 " 13 5 ---[n—-2]n we“ ‘5“ +0 «I: For I sin": dar, proceed as shown above. = akin": — %slﬂ5£ + C CI 3. Jamar was: dz = sins: cost: (can 7: dz] 7.3 Trigonometri: Methods. Page 4-1? 3 = r — ain‘r’zﬂmt u: [sin 1. Convert Elna-1: = a]. — our: 22) and t: a _ a _ ‘ I. c0521“ = a1 + ma 2:) and substitute into the (H ) d" m given integral. = L—ein": — Janina: + C 2. Peel oil“ a factor of eecia: from the integrand and then nee the fundamental Identity 9. Ia.wa t sin t [it = Iuwﬁ — d'u] [IRE-Z": sen}: = tan“: + 1 to write the integrand in powers of ten 1:, except for the 994:2: ii: that = —§-n3"‘2 + C wee peeled off. Substitute u = tan n. = —2[coe 1}“? + C 3. Substitute u = a tan a and then integrate the 5 reeultmg Integral 1n trigonometne form. It 10- J‘lmB I a: : it; may help to draw a reference triangle. + ein : 4. Substitute u = a sin 6 and then integrate the = ‘élnl 1 + 35in rE + 0‘ resulting integral in trigonometric form. It may help to draw a. reference triangle. For 11. Jam" ﬁght 2: dz = Ia“ [—du} V'ui - a“, substitute 1.: = a new. 5. Imam-Ila: Imixﬁmrdr) —e°°"+ C 12. {cougar} d: [in + cos 4:) d: z [[1 — n2][du] :1 r+§sin4ay + c =u-1'3E-FC =.}:+§sin4:+c = sin 1: -— §sin5=+ C 13. Jami: m3: d: 1. ﬂ] —ene 2:][1+cne 5. Iain”: a..- = Jammie : £2] = [(1— ﬁt: - dc) rm _I:E 2E3 _ *E‘l‘T I+C 1 ll 2 —%c055\$+ 3:933: - Q06 2+ C 14- Iain 2 dz Iu—ﬁ I _du) a... T. J‘einzx cm;3 dz: = Iain“: can“: (me. tin] = §lfcoe x] _" + G' 15. Jtenﬂﬁdﬁ' = —1|nlcon2ﬂl+C 16. d3: = 21nlee¢§+ tan gl-i- C 1?. Items: em": d: = [mammaxﬁmgs ds} = [(sinlz - ain‘tﬂwe 1‘. it] =jM—«ﬁn a3 Section 13, Trigonometrfc Method: Page 325 {max + Ham-,2: dz: : Itan3dtal1zm+lﬂacczzdrj = J = [um 1) in Mercl=lms 3- =-'§-+ n+ c 1 a l 4 =Ttanat+ tan r+C = Elm 3+ Elan 11+ 0 15. Inert”: tam 2 d1: = Iam‘ﬂsm run 3: d1] 23. I at“ zone: d: = Julia-in _I_ 5 _. 59M: 2+ C m :gﬂ-ﬂn m]4f3+ C 19. [Hangar-Ii 82122:] Jr: “2398:: — 1) dz :4. Jame-1 a: = [m u du =2Lu.n1:— r+G =lnlsucu+tanu1+ C 20. fish: 2+ cossz if: =Igﬂm¢=+m e'|+ C = [(241122 + 25in ECDS : + cos-2:) dz 25. [sainme dz: Heir: n {00911: in) = [Jr—i- Iuin 2: d: Billir+aalgr=1 u_ :2 andaniILsms-Eein‘zr '— zi-sinil? + C =::+%{-couf!=}+C 20. Izm’zdz= xtan s+1n1cos :I+ G : x — 13431523: -1- C Note: Here is an achrnabe {but equivalent] procedure. 21'. [tan‘i sec t d1: [ﬁst-3:62! — 1:12:53: 1 I" IIEsin 3+ cos :32 dz: : [(m51_2m3r_ + m 1} d; = [(singr + 25in :ms z+wairj nix =ﬂim+glaecat d! —2Iaec3t dt+ sec t I“ A = Id:+2]sinz{cmxdx} =§m3ttani-=}Jsec31di+lnlsec1+ Lam ti = r+ 2[1§(sin xﬂ+ C 1 5 5 3 :z+ﬂ[ngx+0 = smitaﬂi—Emitant+gllllsecl+mnﬂ+ C 21. [tannin sex: 1: in = [[scclu a Use: It du 25. [(21426)dﬂ =%lnlcsc 23 — ml; 291+ C = [[Mcau — sec 51}an Formula 423 29. [maroon dz: = - [maﬁa-(v—cacxcol, a: dc} =M—'T—“"L“"“+%Jsecuder-accudu =—51;nsc3::+6' 3!]. [max not“: dz: -%cot"’:+ C 31. Imixcusxdx= [w sin 3 = \$36: :1 tan 1; — %II1[SEI: u + tan uI + C 22. Isa“: d: = [wearseczr d'a: Page 325 =-I[si|1:_1-l-C —m\$+C 32. [tan mach dr: a: =J—EET cos rain .1: 2111 tan[:—r+§) 33. I 4 - Em: [1J4 F amiamma d9] = 41139523 [m :43 + sin 23] + C = 23in" g+§Mt — :‘+ C nix 3-1. _ iii; — a“ I l = sin“; + c By trigonometric substitution: let nt: 3 sin ti. Thtlt dz = 3 can {3 am, and V9~x2=V9—Qsinnﬂ=3maﬂ; I dz _ 3mg»th W" m : a + C=aiu‘1(§)+ G . 2+1 ul-E. :11 21rd: +J dz 2 iii-1+9 34+? =vm+lniat+ WHO By trigonometric substitution: lat .'I: = 2 tall 6'. Then dz = 2 seciﬂ‘ :13, and 1H-l-;1=1H+4tnnl =29ec3; It“ nix: [2mmﬂglam29da] 7m :Zlmﬂmﬂdﬁi-Jsmﬂdﬂ =2mﬂ+lnlsec0+tanﬂl+61 =vm+inﬁm+ﬂ+q =m+1nim+xl+c as. [(Q-H‘P‘mdr Chapter .7, Methods of Intqgratiﬂu, =gnxg q-F+91n{:+ ¢9+¥Jl+c By trigonometric substitution: let a: = 3 tan 9. Then it: 3 sec-2i? W, and 139+?=V§+9tan!ﬂ:3mﬂ; IJ9+FJI= Iamemmw d0] =915¢c3ﬂdﬂ = W+1§1rﬂmcﬁ+mﬂﬂ+q =9[=V;[;i_; 1+§IHHVB + F +§|+ =§:¢W+gln( 9+ +=}—g1na IWHMHWIHG' aw. [aft—J =lnir+x/:“—-H+G By trigunnmutri: substitution: let a: = ﬂ Then 11': = ﬁst-c a tan a as. and W=W=ﬁuﬂﬁ d: _ ﬁmﬁtﬁnﬂdﬁ' iE—?_iW =1mcﬂdﬂ=lnlsuﬂ+tﬂn9|+cl :I x+'zﬂ_7 71" T =lnlg+1xz?_'rIu-§qu+cl =1nim+V12-7|+C d'J: ._ l l I aim-Hm)“ =iﬁtul1_l[‘/Ezj + 6 ti: : - —1 :7 c 39. 9m 76+ ll EL'.‘ + C: ﬂu “'- imﬁ=iiﬂfq Section ?,3. Trigonomerrr'c Methods Page 32? =%m_1(—V;)+C =%ln|secl9+tan0l+0 41.[ if :y 3 + 1+1 +0 :9 4—1“ Jig—(awn? ;?9—(x+1]’ [ Econ-9dr] = . . =1 3+4 [dslngﬂ] -1 — 4&1n29 slhlm + C _ =%Iwc23dﬂ : 46. jv’ahﬁdﬂ Jim 4:“)? J1: I :-%cuLE+C= —___.V4"‘2+C 4: =JI'IJ'1 - siniﬂlﬁtw 3 d5} LEI. 3—1 '.= sin I? rJ'a: 42. f _ :3? + 9 = Imaﬂdﬂ = \$0 + 37511126 + r: =I 3mc23dﬂ “Jana 9t3n9+9 =aaiu_l(z—1}+%(:—1]V2£—xg+0 ,_ J until] dug _' ENE 41.- I J: =I «'r . 59-22% M; —1J=+5 =§Jcscdriﬂ 47—5—“5HW 5Lan€+5 = lmﬂdﬁ=lrﬂmﬂ+mnﬂl+vﬂl —§lnlcuc6'+mt 91+ C I n‘——-——-"'. tg+3l+c —2£+ﬁ 3—] =1 T'FT'I‘C “l 5 5 1 'I‘lmiaamul:te'I||.'l-'LI.LII:I1lining";E — 2:+a+:-1|+ c d: 43- Iﬁﬁ=[m =I'umﬂwnﬂﬂ IAt:—t-¢1=uﬁscc£i 135ml] — 13 =Isecﬂdﬁ=1|ﬂsecﬂ+tanﬂl+cl _ z+4+wJF+8s+3+C _ Gm 313 1 . a = I Bamazﬂdﬂ :Hdg ThismbewritmnaslnlmHHhC dlanﬂ+4 _l v—lr—l -3 _2m ( E )+C 49.1941115331:=Imauaccaudu=%tan4u+c man 45. 9—(r+1] “his: [mgr-i: 50. —%—= ——'—' Junx+wcs Elannz+l __ ﬁwnﬂd‘ﬂ _1_ d6? _1 ‘Ig—usinisWvaVEIMEw Page 3'23 = ital—Ryan] + C = \$751”: ' in}? tan 1*} + G 51. A = mixing: a: = ,1,(§]=% I} HIS 52. m = I we“: J: a: 0.9mm 53. r. L1 L1 56. 53. Eff-i NIB M = I Jams}: drﬂﬁ 0.0373155 r rrf-t 111.3 M,=%I m4: «1: 9:0.CIIESIJSQ wfd. (a?) as (-1.90, 0.19) ” r3 _ I 1 .— V_ er’nm 1: d:_ T 53 15-5031 0 a4. aﬁt] = sing! um = Iain“: d: = y - gm: + c um]=%(ﬂ] — isinﬂ+0=l€=2 w 2 5(1):“? — %sin2t+ 21d£=3f+21r 31835 0 IN] +cas :dx=[ 2magd: = Jﬁ‘coa gldx: i2ﬂsin§r+ 0 [sin Brain 5: dz: Jamalt-rﬂt) — con-5:} d1: —:"-sin[ —-'2:::I —- ﬁsh} 32 + C = %sin 2: — ﬁsin 31-F- C Ices sin 2: dz: = [1}[sin[gz}+ sing 3]] dz = —%ms[§x} - %cm[§=] + C Jena 7: mu( - ﬂzlsin 44: d: = [ﬂeas 10: + cos 4.1:]sin 42 :1: Chapter 3', Methods affair:ng ' = IiilsinE—ﬁz) + sin1421+§sin as} a: = [{Hﬂini - M + sin Ht] + {-ain 31'} ﬁ- = ﬁlq’C‘JS'E-ﬁﬁj - 515cm 14:: — 315mg: aﬁcos 6:: — 3113:1019 Ha: — ﬁnes 33+ 0 59. Isinli‘l: cos 4:: If: : [£1 — cos Ethane 1 _ [Ewan - Ill-[cos ‘21: + :06 10:1} dz '- = gain 4: — 1gain '21: —n Tlﬁain H]: + C “a. fll‘ = =}fr {gr- d': = I—atan 1'] d: In fl =%1I'IIDOB .1:I+ 01 f': 01.1“ch I’m} = 1 = 0.50:" = V‘coa : If: J‘f1+[1fws:h2dx u :12 :I 2:05:13“: 2 u 5 rd: 61' In—E— 9— '_.¢!t'.|1=\.llli--—z2;u2=£i—-z2 ' = -I d"1=_1rwg—?— 1|+c u— fh—u—du 1.! —H. 7.4 Hﬂhod of Partial Fractions, Pages-\$55415? 1 I _-“‘I+ A2 ' :{3_ EJ—T 1._§ 1: Ad: 11 3} + Air Hr: u. then .41 :7}; if: = :3. than A, Thus. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern