Calculus Third Editon By Strauss, Bradley and Smith sec7.1

Calculus (3rd Edition)

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fig: 31'! Chlpter 3", Method: of integratin- . 1 . 1 li'lntegratiun . 1.1 F n :_ a: 2 = J‘fl_1dfl=llflfll+ C Nol::i}0linnl =‘—:F+3={=?—1] ".=']n{r‘ — 2:? +3] + C = 2t:z +-~5 It J a gflté‘ - 2:“ + 3}‘=[(4;3 - 4:] fl'fl =' H a" £1: —1-(:‘ — 29+3J“+G _~ .5':EE'__@'-J‘_{:‘ + 4: + a] ‘ 1K2: + ‘11 d1] =="In|:’ + dx+3l + G -- d 1.1. E]: FI+=+1 J: 2 I + a: + Ill—llmrri- 1} dz] 4 rich-1.... . . w filfl(l2+l+1]+c [33% u = fl _ __ _ 1H: _‘ ‘ p. In. 1—4:] a: E _ I It“ . . J“ _ zJ—flllzt _ 1} dz] 9+9“? - I%:—'113(:I—:}‘1+G it _ [Manama-is . ‘3' 1373—?- a —'mq" =I—u4d'u gg-I'c a -, . =—§(1+mt=]5+c 14' [W 'W SICHM J’J, Review afSubstr'tufian and Integration by Table :lzzflnx—%]+C é-m. [Insd'm - =z]n::-:I:+C =a'_1c"[:—r:_]‘_l+C 5' .[Hifirsfi 25. = r1: — [Eaj-lllilr1+ bc“l+ c 7?; + Jim}? 1- %Inl:+ 9'? + lI-I- C [wit—m lilarmlllfl. + 1 4- ‘—'| 29. If 1 + + m 3"- : ‘T+ '3' 31. Je_ 4’sin 5: d: Fun-mu a. 492 32. : [16+25)_1e_4‘[—4ain 5: — 5cm 5:)+ C —4 sin 51— fimaE-r 2*4-6 41:' [um-1m =I[,_1.=2 —§—ain‘1x+{zv‘1— 9+0 104-51)“th = b_llnll +llzl+ C 515. I: In x d: Formu a 502 ‘M. Page 313' [7—9312 a — =-VG2—zz+C [41mm (2 +135 _ (r+ 1)‘ =---5-- 4 +0 = flaw 11"(u— 11+ 0' Inf—1+“: m =lgl{3£— EJW+E : c‘ ’d': ‘—u 415%: - 34-] + C : 1n 2:: dz Formula. 5112; u = 2 ¥In £5) ={(;)(2=]1(Inl2=|— 3+ 0 i'gvln 2: — g + C '1’ +6 :3 — {flail-F- =:'[+C' [mam = afln 41:}3 — 3 (In x}? d: F = :(In :33 — [rfh'l 1:] — 2zln z+2151 + c = xlnax — Eztnlt-f-fizln .1: — 63-!- C [13“ Jézi+1 fiju_u2 in. 1. Few + 11'” + c l—II—I [I '—'—i —J *F Fag: 314 Chapter 3', Methods of Integration :14. J—E—M d1: Formula WEI; u = 2: Iuinsx ms‘r ch: = Iainiz: c0343: {sin 1: dz] 1f? _ ‘2 q — =\!¢1?.+1—In1+ 4 +1+C -—[[1-Cmr}muzl:3Inmdz.-j ix = Jms‘x (sin 2: dz] — Icon“: {sin 1: dz} 35. Inc-2.1%) dz Formula 42? 5 'i" : —Iu4du+JnEdu= —£5-+-¥‘,-+G _ g z :r z -sec2tan§+1nlacc§+tanfil+fl =_%cmar+%wu71+c 35. Jain”: dz {4. Iain”: tong: d1: = [1— am; 2t][1+cns ‘23:) d: = —EBiI15IC03 J: 1- gfasin‘: 11': = — errant] d: : i—Iainih: dz __lrfi . 53_sin2: sin-1r _11_1- ._ 33m aromz+g[r 4 +—M—]+C —_a{§: gsm-ias)+0 I'ormuafifil =§ W fish 413+ C = —&sinsx mu z+ fir—fisin2r+ “fisin 43+ C j d 415. lfrrlisodd.1ct u = cos a If n is odd, let 3? [Tn—“4' = mm 1.; = sin 1:. “both an and r1 are men, use the 9 + E: + 1 [3: + I) identities shown in Problems 41] and 4] until _ _ 1 + 0 one exponan is odd. '- 3E3r+1 :- l 46. Let u = c‘fl; du = if” da: 33. [(g—flmdz 1“ 3 2 = IK'JHIEJI +2m9—fi1’2 =2J'I%=E[u-IHI1+HI+C 4 E +%§sin_ + C :25": — 2!n[1+erfl}+0 ginia: a I I I r 3!]. Iufifi 15: _urmu|a .182 or use |_enLItI-25 4T. Lat u : :1“; d“ = %rnafld: Z + a: = - ' 1 t. I E c — smx+ “I a“(§+4) + = [4.9 “HIE—«‘11; Formula“ H + 4|}- Iainaz d2: : d: 2 u+u 2 . : (“7+1_ 2(uJ-4-l]+lnlu+l|]+cl =%3 _ ésin2z+ C =4['§u2+u+% — 2n-2+lnlu+l|]+ cl =%3‘ — %3E11 2:+ C 41. JcmadnJl—Lciyfid, =4Eu2—u+lnlu+1[l-I—C ' 12 =vls= +%B-—g—"12:+ C = 52;— — It“ +1I1(::”" +1]]+ C 1 I' : —.r:+-sm 23+ C «1d: _ 6. _ a ' 2 ‘ 43. I—F—wgrlz Iatr—u,dfi:_fiu til: i 42. Lctu = sins, that = matrix“, 5 _ I 4mm] _ 24 m i [sin‘xcoardr = %—+0 = isin5x+fl _ 1;"! + 24:3 _ u2 + 2a: '13. Lat 11 = cos :. du = —ain 1dr. '_' 2" lg" d1; _ W4“ W2 muld use Formula 44 from the Sludcm! Section 12!. Review of Subslr'tutl'an and Integration by Table Page 3J5 gls} _ «ng(%) Mathematics Handbook (or other table of = x 0 _fl_— integrals], but ainec the degree of the 9 numeth is greater than the degree of the _ 3| I _ sflfl “1 9c. denominator, do long division to obtain: _ T E a I 81 9 lflrl 1__ E =-:1-1r-§'K{ln9[l—]nfl] MIG“ 4“ + fi inf—1)“ 81 _ n3 u: n ] = T! — 91? In 1|] F: GILES- —2v1(f—-3—+E—mln|2u+ll)-l-C i __ 132; f3 Jana lffi ‘ _ 4:. Jr] + 3:1 Int}: + l] + C at V: “Illa ; Eff-1.12 dx 1% Lana! Mezt u '49. j—-—r d: (2 + Lanai) I Let. u = 2 + tan :3. tanzt 396:2! d: = wJ'EU _ 3231!? «I You could use Formuta. 152 from the Student Mathematics Handinok (or other table of integrals}; inntead. let :r = sin f}, it = coal? Jr? and 1— §=coafl;i[z=0,thenfl=fl andifx: 1,3: 9’2: 113'! v: «I sinia on: 90;an an) El “N 2 amines) = 11']- 4 Jill 4 _. l 1,:‘3 55. V—21!1{7;(1+ VG) ]d: 1 = 21J’fi(l+ vial-’3 a: J = gases «ii/5 — as W} 9: 40.3053 Use it 2 1+ J; or amlculstor 2 2 55. v: rrIHVfi— F)“ dy: «In # 923.1” dy 1 1 Forrnu a. 231 _ 21;: 2 = fl‘g—‘iy—J—‘FgfljD-l%] 1 =05 Page 315 = aha-1x — 31,15} :3 3.3590 51'. ty' = "‘[In t]: — a? (In)? —x‘ _ __?__ 1;: 2 1:2 5:] 1+v“i:;l-l=—J.!flf!dt Iji If! u =1n 1:; d1: = Q? J: or acalcuintor = Fyfifi = gluzfl :3 0.1207 1!! 58. dy: -EL‘;:de= --tanzdr, da=Vl+tanlzdz.-_-sec:de 1r,“ 5: Jamxdx=lnleeez+tau IHKS‘ IJ =ln(l + «fly a: 0.8814 59. d3: \g‘l +4? chi; dS=2ryds I 2 2 s: zxjéy’l-H? d1: = 2:]“Tv’1+u*(%) I] I} Formula 17': 1.: r: 2: _ If“? +1331” m uh? +1314” 4 d E 3 4%! u+[u"+1‘ll"2]) u 9J5, :Intfim) 15 ' T2— Or, by calculator S as 3.8!]91' GD. nip—:2: dz; ds=1,-"1+«i::I dz; d3=2nuda 1 flew—7H4 as {J = 3%)(1 + 4333321; = $151.13 — 1} Or, by calculator. 3 =2 5.33011 Chapter I. Methods of {Meg-refine —cuc mfmz+cot fill 61. Imed':=-—[ mx+mt= = —1n]eacx+cotrl+ C 62. a. I25in£mstdr= —2J'uos.v(-sin: = —2{1fi)coa2:+ CI = emszz+ OK I b. J-‘lainrcoa :dz:2[aiu :{coexds} = 2(%}ain2:+ c2 = sin“: + c: c. Jflainxmrdr=Iaiuizdx = —}§cou2£+ C: d. All three are the same with C1 = Cf!- 62:03 _ IE1 =Ga+%u 63. Letu=sr—::,d'u:—d'1:. Thcnsin== 11' D Isflain :] dz=J.(1r — ujflain u]{-— Eu) 3' D [-11- - u) ffsin «Nu 1r Kain u} du — [1: Hail: 1:] du 13 The value of the integral is independent of variable used 30 I I = «lflsfin .13} d3: — lzfluin x) 6.1: Add the second integral Lo both sides and divide by 2 to obtain the desired result. E4. The surface area S or the torus is the sum area 5'1 generated I tating the top of circley= i: + V1 — 915 about them the area 3:, generated by rotating the be D"—'|=l CF—IH y=b— 1— z’aboutLhcsameaxia. either case, dy lxl ‘.'I 1 :1 = “(35 +(Ul-E) 1+? Wehm'm S: 31+S; =12!” + FEM/1:37? a: Section F2. Integration by Part: Jr]. 2:“ — m; XfiL-Fdr 1 “I _ 41b . —] 1 _ d1: = arbsm II J 1 — :2 #1 ...
View Full Document

This document was uploaded on 01/24/2008.

Page1 / 6

Calculus Third Editon By Strauss, Bradley and Smith sec7.1...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online