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# Ch.2 3339

UH

GPA 3.0

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This 16 page Class Notes was uploaded by Jade Martinez on Wednesday January 28, 2015. The Class Notes belongs to 3339 at University of Houston taught by Dr. papadakis in Spring2015. Since its upload, it has received 206 views. For similar materials see statistics for the sciences in Math at University of Houston.

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Date Created: 01/28/15

Sections 84 85 WNC39 a 5mm 21 M 4 Ursub bL A L39WMUU r 7 1 1 x V 0M XL 004 WWW K0 Example Evaluate f 39C4x 113112 x dx 3 gem 10 5470 W 1 m H k quot x L 13 S RU x if 391 A a a gt4 53 quot MN bL Uxub r i F 3 A W W W i m a La j mquot 4r quot ILLI39 3 4 K 1 q 4 quot m A quotr j A r a 39mr 1 r tow I UL 7 N 2 f2 k 1 3 a 1 394 M 7 t1 i I ij 37 i r Elf amp rrw q 3 1 I r quotHr PM 7 L 83 Powers and Products of Trig Functions Strategy for tangent and secant f tanm 36 sec x dx We wish to use 1 tan2 x sec2x and u substitution If n is even a f tanmx sec xdx f tanmx secn39ZCX sec2x dx and we can apply the Pythagorean identity to secn ZOC since 11 2 is even K x n WWW let Cyew tanmx sec xdx f tanmquot1x secn 1xsecx tanxdx I and we can apply the Pythagorean identity to tanm 1x since 771 1 is even if neither 0f the above then m is even and we can apply the Pythagerean identity to tanmx 39 W 2 3ampan K Wt b M Evaluate g f WM 1200 L M M f tan32xdx 3 L W 3 UN 39 W u 7 f x 3930quot w x 5 Sam m 3amp1 L730 Wham M 3 w v 9 Z Sc wow Smth 3amp1 m Mr w 39m M h A 39 I Wm H 39 I y W mm a gammch V Vm m OLAquot 3 CL I L 1 ka 39 w MW 5 m KL Um V me WW 854 Trigonometric Substitution BWSWWV 07D How might an expression Ike V612 x3 how up g mm m mes N Mm 40 WW DMOP W ukc H W M Kim D M M at N won Evaluate the integral Supposing a gt 0 is a constant i 6 fxaz x2 dx ICOL 0 80146069 W 39L a m 5 9 30 9770 L Gib 0 w 3 U sitter Lot w ta oe 39 X H mm N 1 w W Nquot Row M a 5 w WWW U93 gay 08 LNKLWWKW 0 4 by Kkkm 4K0 va fig Fquot Six um mmm a H 39 3 3 11836 it 997 01 ietwomm a 0 W W WW W231 2 51quot G xx Mg x Nt Kw m 010w mm lm KW How might an expression like W show up xumw mx WNW V In 4 139 wcnhi A 591 Ang a 9 t lt w A M 1 gE iV j EWi fiifxx39k a aw M43 f M16 ah km ox bu U9 WW CW I llr quot H A lt l i i kg 239 a M xx A u z g39 M y K I 0 quot mw 74 N x 1 a y v2 Na E1quot quot I 3339 1 i 391 f Lqu 74 9 3quot A 47 g f 9 s 1 2quot 4 mpg h gt M I V 1 2 A 1 A w NC 9 L 11 13 SarV quotP g s M 631mm mg a 631 0 quotquotAA 1 M Wm WM 611 0 7 mum Lem WM 0 4 1 02quot Lemur CK a 9 I quelsuoa e s 0 lt n Bugwnsse 39BJBalug am memeg 6 gm k Q g W i V5 Wm 63k or If we encountered the foilowing integral aw 5 H j 3 2 d 72 Kp i X 96 ijz x j nyx we WW haw to Evauai itam A A 39 W4 2N 39 I 2 g 7 ng 5 r 5 WM V vb wquot A of 7 NJ A e 39 I r j 4 quotF g if we had found a common denomirmtor mf m w k o A v 5 veequg g 3 2 gpk fw Md 3 211 1 5 7 W x x 1quot via ax 2quot Ki w gt4 Rowe 2 quot A a J We worst a way to undo ndia lg a atommon denominator becauee we might be able to integrate the k generate fractions as above M ll A a ll llliecizlmpose a propar ralltiomal function Errata goartial fractional lljloaggllle 4W4 anectillon lil5 ll proper rational funmion loan Baa wriiien uniquely as a sum oi fractions of tha fOl l Tquotl x m 60k an x2 bx l 0W 139quot 1 1 y39ig H u v lhesa are rolled oartial frailtlons xi mm ng will y lI iii ilacida if any othar method of integration will work 21 If lhe raiional funmion is imgaropar perform long division Ell BEECOWHZEOSE 39i39ihe rrsrmaino39er into partial fractions aging izilne following terzhniqoes a 4 all y A i 1 all Earzh diainnci factor of me form a a givaa rise to a farm of the Form a lil Its gaartlal framtion decoi npoaitioni liixarnlrlle alive the partial fraction dammpositlan of 1 H l I l g LEMf V s Jr 5 quot A V 1 m I a f 139 53 fquote 4 1i39rquot iv quot339 via a i fix aquot 5 z quot n v39 a J m 1 3w I 39 M a ll a 1 a v l l l a l 539 l g A u l i if g 5 15 quot39 EEEMCIh rergzzseatm facr zsazpr of the fastrm ix W gwes Wise ta an epressjaiion mat the form 141 142 AR a x agt W m its zpartiazi fraaizr on akg ecogwaposii on EiEixa muggnnle i ve the pamial fvactim de zorn m i tic X 439 L V01 m 7 bunquot 4quot g L AU V X V 5L c dfquot 5693 We WM w u Maps mm BL We WWWVW WW I 693 W W x quot 391 K k CD 1 6 4T CU A39 if N r 1 f a 7 a I P A 1 a y A M 33139 r in ij M o 00539 gfwmw 39 F MU SYIWSNS WK mama 2 W2quot a w anEgL M 5 Lusromm in 6 MM pwmmu e w quotJLLMMMQ Cw gm 39 v E KI4439 in 1m 0m mumi 0v mmg mmg h mLMquot chum H T141 111 mmm mmomm WNW SMWWMJM mm mm ampmmmwlgigmmampm m m m m won 39 T i IA mmmm V was miquot ipj 0dr UM YJN a cam 1w U pwaIfMt 0Equot Egg mm 2 ge E e 2 waving h WZEmQQ E a f miljm mi v TwMgum is mum mi iapLUCELULL hN li m irg m ijf Wm h M Eg m t bh ycmTW f mq E f f h V l T aF m MNMNOU o WW mom I 7 9 v LR N r U LknLH L n U anH L 1 DJ LR i L Uri DJ K VUIW I I L 7 V 0 ML ANS L 4 3 9le 39 W513 ZUHWSI N g mz Sm 39 5 7 gm 0Llo6 SD 8 n U733 Me bur W W 2 n leguan W U N w 5Uquot a 0 0quot FL 9 5 LE 7 7 31 t 39 39 0quot H b NM 3 m lt Mu emu m MW WJQMMLmMWS rm mm huge 27 535 EBMQ WMM 39 My Wah f D mm M S mamksu M946 93916 Wt rs IO MM 3 a r 2 39 ELL 0 QWOLD WK W W M r 39 2 w ummux w vaP x Elam Hci a quot A rm w F 47 W U u btmlgrmmmv a H e F ML 395 t X 5 Cr WWquot 39 W M 125 KL M w vm ng gwj 7 WW 9 quot edmcmm and u E KUSA 39g i m f rEWETME EE Q x x gumguwLgmg mummgk k i fhwwq kwwxum 37 i ii h wman mg g A 7 AL f0 r r r M A MW W aRMM 39K i h OffM u r git a N af ia TBLQ p Wamm bmm w NWWLMM W

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