Improper Integrals - JHPNDFER INTEG'RHLS : W555 cane w...

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Unformatted text preview: JHPNDFER INTEG'RHLS : W555 cane w SEVEAML FLA chs : ! -—— cowswfil?’ FOR exams, y = Put) = x2. INTEGRINE Pm oven {5-0 J z .0 F .0 S Pm)sz S #Jx : -;‘LI Now wanes mar nits fifflkoncrlss I as 1-» co ; [m S! J‘Jx - l 14" l x1 rnywa ms sans mm; m y: 3"" ’ HowEvER, ewes 31 it]! = In! mun 1m; 4960 as few, we (mu. wmrE THESE umrs AS wmcmzs win! 1%) UPPER Half a; mrssmnom 0F “ ov' am can. mm " :nptwea mrEakflzs’ '1 nemmnm : TUE wrapper: mrwrm. 9f Par) oust: my > IS DEFINED TD .86 °° J? S Fme = lm 3pm.)ch n- .e—v” a w IF THE UNIT EXISTS) S Put.in 15 5310 1y CONVERGE. IF a; m ” THE umr Doss Nor 5x151, S {~1me :5 saw 72> mama-5 _ “I m S 35"" CONVERGES‘ (amour; vfiLuEIs I ) E. C. I an S 4—4:: amt-MES I noRE EXIMPLES . .0 a l. S ",'.,"'sz>( 7: lm WJX : Ln flrcmmxl 0 2—9” D 3—!” 0 = 1m car-chm! —Arc}moo) : lm rat-chm! 1-4:” 3 a If c 50 m6 lN'lEGKHL camvsgcas ) Q ' J a. -——— x S at” (4:5 HBVE HLREHD/ SEEN THITJ' THIS DWERGES COHEN P -'-' I 50 006 Now fissuns P 1* l. °° 17 -pH 1 S -';Jx = Im S x'PJx -.: m rid—{x ) 1 x 1-9" . 1—)" P I 1-1, a --’-—- Im (.e — r ) up 1‘,” ms umr EJUSTS om)! was» 1-): <0 ’ 1.6., p > I (REnEnEER “1’ mm but? 8853550011116 p¢ a ) mm m 17m 0656 1 a» o 931—,” So °° : J .1. ) . .1. mu H S F X "‘ '-P -‘ w P I . I "’05 comvstrassw 5:“; IF P H ’ S“ #Jx { DWEEGES‘ IF PS I do x I " —x % u—x)e Ax : ‘m S “qua x = a 1—7“ a A: P): darn! Jx dfll“ 'JX Ar= ~54: - 2 f - [In [ 41-303"! -— S e XJX J : 14,60 0 a! n ’e 3-; . [m [if-1M3 H +exl )3 lnnL7+l+e -1] o a 1—9” £4” 1" J— sr " ‘ ha 1: :5- " 81] = 0+0 : o (.l LamrflylfiammLs 1-9” DI NOTE I HFE’E '5 H000 WIS INTEGRBL ENDS' UP BEING ZEE’O . Y (0,3) I X up) SMILBRLY’ ONE DEFINES b L 8 Feme = llfl 8 pucle 4t .00 ‘64-” r. canvERGES‘ IF me unrr EXIST; nwo DNERGES omERwlsE ) 0 . 'J - ln ° ——J—~J - 5.6., S W x“ ‘ “’11, Y - -m 4"” 1m Arc/moxie: 1m mimo-m-JM)= flan-'4" .R 44'” lm L—nrclamfl) : -L-E) : 23: £44” LcomvE-IPGES ) meLY , wE DEFINE go 900ch = 8:530:17: + {,chflx «mm: c :5 any REM. monster: wwouy 719KB» was 0 )_ no 8 {-1.me IS smp 1p .Q CONVEIM‘E IF DNERGE OWRWISE , M 8 Fund): wvaREE 0m) 1? c. a. Bow 8 {~2wa we no a ’ “a I I fl.“ a... 5.6.) 8 WJX 3 8 "xtJXI- S “1‘45: -w _m o 3. f 4' f 3""- C CONVERGES > , a more: S Funlx .5 Nor msnns mm; 99 m .Q gnu—— t 1"?” at w «2 F01? exams S xe = M MIx 3 1m ’ 3*” 1a” 0 9 ha incl 1a” W S x Jx DIUE'RGES . @ HOWEVER ’ t t 1 Ln Sxe 2 lm fix] .b-‘bw wt t4” -t zw—L - t =. 1m 0 lm L351: (1:) ) two I! mess Bu. COUNT as WE FIRST " TYPE " 0F mmomsre INTEGRAL ( momma-E 1.117113 0F wmcmnou J. Now (05 7mm 70 ms Sé‘coruo " TYPE " , I cowsmen, FOR exanms, sz) sf}; ow MEL ‘1 ~01 mnmuws on) £20,!) so u . n I .._’... Has no: yer BEEN DEFINED, S r, J! O (0,!) HDwEVER’ Fan fimy I no o «04 l l .9 l (’ “a ,4: S fidx -.-. 8 (1-30 x : ~J'I/l-X ‘ 0 o -_- ~2Jl-l +1, 8N0 I [m S fidx : lm_ (“iv/Ia! *1) = 4., 1..., 1“ a ' 1-9! .1 I N we wlLL DEFINE S 3.5—; Jx w 136 ms LlflIT. HOPE GENERBLLY ) DEFINITIoNS : IF put) IS comnmuoos on) Kayla), BUT p“; __., tea as x -» b“ , Wu 7715 mmoyere INTEGIMLEF 3.x) ovaa [a,LJ Is .0 S: fixydx = flirt); S“ Fme . b IF WE LMIT axag-rs, m5» S 1&an :9 SAID TD COMUElME; a. OTHERwlSE IT 55 53m 70 0105965. 1 .__... L TD .2 S W; Jx Comueeses ) 0 E'C‘ } sanuwmy ’ 4' Fun) cmnmuous OM cm!) , 3w Pu) 4’ tea as x-yq b B 3 F1.an = ha 8 FLXJJX m $474+ & ch) comm-00095 on) [4.53 EXCEPT .97 x=C no 0&5) erERE IT 81.0105 uP, THEN b a b 3 1%an = S Put)ch # g FLxJJx a. a. L wars : son] or TIIESE fiRE IOProPER ""'"" b mmmms man 8 Fme Com/Elms: a :F moo ONLV a: 11197 80174 COIWERCE, NOTE : HNY 6908103877010 0F mi BEOVE Types IS 91.50 POSSIBLE) 6.6., m ._..__1_._.. Jx 8 1670‘“) a I :s anPRoPER Fan Two 26350»: < UP?“ “0'7 °° ’9’” {32"me sums up a? x = 0 ). EXBDPLE 5 : I“! 1 z 1 8 all: t. I“) g .J—Jx ,___ I“, _ Inn-x" = ' 4"” K 441* 4, Mn (4 {nil-.21 4- Inn—£1) : jam“ lm In )ch1 mm» w5§m15xasr '50 THE INTEGRHL 01052655, H a. _ 3: q __ 3. .1 8 dx, = X Lx-z) 34x 4. X Lx-z) Jx ' (ac-2)” i a 1 '9 a: I H “.2- : Inn 8 Um) 34x 4- lm \ u-z) gal): 1-9-1“ ‘ «Pa-3.2+ I; J. I g, '1 : lm But-Us, 4- [m + Shh-1) ) 1—9.2." ‘ age-’90. '6 .l .L = 1m [312-0343] + Inn; [SW—BLQ-afij 4-52? L»: 0 [a-r3] «r [Jig—o] 3 = 3 L '4 so ' .___'___. J .—-—‘—-—-- Jx —--——-'-——-'JX 2‘ S W(‘+-x) x + S f;(HX) fin”) a s M315 r I camp as Rspmcso 8y nwmwe no t a,” ) , ASIDE : LET'S DO THE (MDEFINITE lNTE'GIML FIRST. ..____L__—. : S I J‘Jx fifth?!) Hui)" ff: 1 I J 3 o--' x l 3 Huff)" if!" Jar-HG? d.“ 2 z ,1 M =¢nrJa~M+c = QHmIHMfi? +C. I i J I —-——- 4x : lm ~———- (film) ##04 & RUN) « z (m .ZHFCIWR’J; 1140* 2 lm Lana-Jan! —.znm‘nvfi) .PL-w 1 1L :5- )“ 0 3 a. U Io, 1-9” .e—aco -I- I 4‘5)‘4(¥)= Tr a. ' a. 77305 ’ m—J—Mcix : 35+ i :— 1T SV‘YUH) ‘- O :1: I 2 a " z I.” 33.2.14, 0 t—hmx 14,5“ 01-h»)! : 195105: 3 sMde =~decuadnml+c 1-5m: “=1'A9NV ‘ :—'nIl-Inuxl+c dus-QectXJx' :3. 9|?ch J l I I, I” - Somx'lgg."*”,— (m (“It’ll-knoll + lull—Irma!) I- 1-9” “’HICH Doss MDT 5x157 BECIM‘E 17:5 FIRST renn firmware; — In [ml 5'6 ‘ 7716 INTEGML owewes _ ...
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This note was uploaded on 10/23/2011 for the course MATHEMATIC 221 taught by Professor Staff during the Fall '09 term at East West University, Chicago.

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Improper Integrals - JHPNDFER INTEG'RHLS : W555 cane w...

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