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# Calculus II MATH 2242

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This 9 page Class Notes was uploaded by Anibal Schmidt on Monday October 12, 2015. The Class Notes belongs to MATH 2242 at Georgia Southern University taught by Francois Ziegler in Fall. Since its upload, it has received 83 views. For similar materials see /class/222041/math-2242-georgia-southern-university in Mathematics (M) at Georgia Southern University.

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Date Created: 10/12/15

Math 2242 Review 2 Name F Ziegler Spring 2009 Show your work to receive credit7 and your nal answer in every computation 1 Connect each integral on the left with the rst step you should take to compute it sin2xcos4xdx o 0 split into the sum of two integrals 6 1 2 dm 0 o substitution m 71 71 d o o inte ration b arts coszz m g y p 5m d b idz o 0 re eate inte ration arts W p g y p complete the square cos 1mdz o 1 d o 0 long division 7 1 V 2m 7 m2 sin2z cos3xdz o 0 partial fraction decomposition 2m 1 l l dm 0 o spllt off one cos1ne factor v1 7 m2 52m cos3xdz o 0 double angle formula sin2 x cos3 x dm 0 o trigonometric substitution dm 0 o product to sum formula 1 1 7 0 know it as a basic building block 1 dz x2m2 1 3 A B C D 2 a Find the coef cients A7 B7 0 D such that i i i 952 1 252 1 952 1 2x43 b Give the partial fraction decomposition of W only leave coe icients as letters in form 3 Compute the inde nite integrals a 2 cos x dx d b x273x2 tanGx d C Cos4x z 4 Compute the de nite integrals a Asgdx b 2 7 71 dz 7r4 c cos4 x dx 0 7r2 d em cos x dx 0 5 Determine whether each of the following integrals converges or diverges If it con verges7 compute its value a xe 2 dx 1 Math 2242 F Ziegler Review 2 Show your work to receive credit and your Name Spring 2009 nal answer in every computation 1 Connect each integral on the left with the first step you should take to compute it sin2 9 cos4 a dzr x6 1 m2 1 1 cos2 9 dd e3 d3 Veil 9 cosquot1r d1 1 dm v23 32 sin2m cos3m d2 2 1 in m e2 cos3x dz sin2 cc cos3 x d2 d3 2m2 x21w13 1 dr m2x2 1 dm 2 a Find the coef cients A B C D such that x3 Ax8xzl Cx 1 AXE Bx AWN quot4 u H N l 0 0 split into the sum of two integrals substitution integration by parts repeated integration by parts complete the square long division partial fraction decomposition split off one cosine factor double angle formula trigonometric substitution product tosum formula know it as a basic building block x3 AxB CmD 33212 21 x21239 5D l u 0 0 I 0 243 Give the partial fraction decomposition of only leave coefficients as letters ZXH3 x1xl7 gtlt1 132XH quot x A E we neg 422 5 2 in form 23050 7 ExF KH quot04 2quot I xI 4 WM W17 d 7 nt II nly39lA uv wha 7 0 Mse w 3 Compute the inde nite integrals a E2COSL39d 3 I X2 SWLX 4 ZXCOSK quot ZSIWLK quoti C 39003 e ii 0 f 52113632123 0 EFLquot 43 X X A game5 Ll l f X m F B X IWJKZ 39 Z 739 x n x z ail 2 0W SLO x zri quotmu r A Witt 3E tan6 a C 00543 S aM 6 1 m c tow x S D aLx t cus x g 1E 3L 4 Compute the de nite integrals Ins 8 mg THE AILamt 451M It a S quotArest Mb 0 it So m Iv HEW 1T 1quot X 1 SB l lot 4rnntvtn Q OLX 45nd Guiltquot lx uczqmei 4 eqoo W rm 1395 X h Ax Iquot 8xv04 C m xzan k32Ax A3811 I O l 3 39 A 3 I3927T1 L X B 2 b a13dm Si x l 0015 0 0310 C2 393 i w I r W2 ML i Z x I 04 0 03 K KIX I K 11212 ZIJqlZ kz if 774 l 7 c O 0084xdx S dx 3 lZLoSZXOoSzzXdx o 0 WI X SMZX Sigiiiatx 1 L x 45th l 35 Mquot f 2 x 3 a i SmZ SM rK quotPM 3 t 8XTquot imo 39quotquot quot1LOOoo rm Fz 7r2 d 0 excosxda 7 6X slhx exusx S n 6Xcosxd x rm 2 SO 4 stde 2 x SMXrtogx Smx 1m 7m 0 39 quot ecosx x e Io 51 i quot at 22 lt gtf TH2 o ITZ H 5 Determine whether each of the following integrals converges or diverges If it con verges compute its value 00 2 quotK I a 1 rue 1 d2 2 8X9 dX 39EgeudM quot euFC uz x L X1 b 1 52594 2 is 0 quot l lt39L l 5 l quot H S xe 0W 26 1 quot 26 26 w egotx In 7 l 5 X g 29 cggjw 0 2e Math 2242 Review 1 Name F Ziegler Spring 2009 Show your work to receive credlit7 and your nal answer in every computation 1 Find the length of each curve a my cos t7t sin t with 0 g t g 7139 b y17x2 withi x 2 Set up7 but do not evaluate7 an integral for the area of the surface obtained by rotating each curve about the y aXis a ylnz withi x b my 17 cos tt 7 sint with 0 g t g 27139 3 Find the derivative f l 17 where a fx361 b fx tan z 4 Compute the derivatives a sinlnz b 1nx2 2 1 C ecosm e 10g2tan 196 f sin 1cosz 5 Compute the inde nite integrals a z 1122 b Sinx Ch 3 cos x 61 d c 3W x d 1172dz 6 Compute the de nite integrals a 012t t2 dt b 07r1Costdt 7r2 C Co 2 dx 0 1 Sln z 2 Sdz d 2 1 z 22

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