30
Dec

integration of exponential functions pdf

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/Subtype /Link ?^lQtBCAE8(uP"mMNPC^-hF7E="p[=I&0RZF)gmV_(M\@:1[j^OrMMVIL\.mZIRO8Z.cWjFS[O_"!mfZDrqEE;G&Iho655('k\ud][0D7H/.>CS]pRJ^eQAh"NDUNH[IgpGjmUCSXa%MZ8/1mnkPeI_bTXRE0U7F:3Johl96QMVI)5]&jj+3D'P>1@jDlt4"ZSj@62d\^tdSP@cebp.Ql(.B8ns,HrBkd179Bi"52GZf,?>F9HUeBsCQ8VN.P[8->o7RZA#U+j4;OS\b:LJt~>endstream /Length 6180 /ColorSpace /DeviceRGB Recognize the derivative and integral of the exponential function. /Height 100 /ColorSpace /DeviceRGB % 'FormXob.706a4adf6192e00b64f6556e0a16ed22': class PDFImageXObject 21 0 obj 24 0 obj We’ve shown that differentiating the exponential function just multiplies it by the constant in the exponent, that is to say, d d x e a x = a e a x. /FormXob.bbd1139ea6c1056ac849dce070b1ce9d 11 0 R /ColorSpace /DeviceRGB /Filter [ /ASCII85Decode The integration is part of the important concepts that associate with mathematic, and is part of the main operations in calculus. /Type /XObject 595.2756 /ProcSet [ /PDF We’ve shown that differentiating the exponential function just multiplies it by the constant in the exponent, that is to say, ax ax. Integration Techniques Worksheet. Prove properties of logarithms and exponential functions using integrals. h�\Rak�0�+��]��� ���6�~�2c2j@[i����r�:;�5w���K�)���T���d���ݛ�~��~鍷�1 �b��� ��"��6��0���j�>��D�����������)g;Su�Κ�O&���&���ID��=6fo�l]8��uO��7;�)�jg��ɚOWW��ͱ! %���� ReportLab Generated PDF document http://www.reportlab.com 24 0 R ] 25 0 obj For example, f(x)=3x is an exponential function, and g(x)=(4 17) x is an exponential function. /Width 357 >> 25 0 obj endobj /FormXob.d7477e114638f2c471ec4a55453def9f 12 0 R Exponential functions occur frequently in physical sciences, so it can be very helpful to be able to integrate them. /ColorSpace /DeviceRGB /ColorSpace /DeviceRGB << /BitsPerComponent 8 % 'FormXob.9beb123a9d65cff433a6c59c3520a4fe': class PDFImageXObject % 'FormXob.714905f6842e063ca4ffcc2eec80bee2': class PDFImageXObject 0 View Math147 _lesson 5 Integration of Exponential Function.pdf from MATH 147 at Mapúa Institute of Technology. endobj /Subtype /Link /Subtype /Image /Subtype /Image /Width 233 >> /Height 93 % 'Annot.NUMBER6': class PDFDictionary /ColorSpace /DeviceRGB << /BitsPerComponent 8 25 0 obj /FormXob.d0ad280a0e6d51989bdc78d7f1afc991 17 0 R /FormXob.dce2fe057584215fb743584ad2229fb1 22 0 R % 'FormXob.51afb6fcee6da4fb19fc583658f41bb1': class PDFImageXObject /Width 1020 >> 10 0 obj << /BitsPerComponent 8 /Height 93 4 0 obj 21 0 obj /URI (http://en.wikipedia.org/w/index.php?title=Error_function) >> /ColorSpace /DeviceRGB *Qendstream 3 0 R << /BitsPerComponent 8 << /BitsPerComponent 8 /Type /Annot >> The function f(x) = 1x is just the constant function f(x) = 1. 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730.9469 % 'FormXob.aee9e3f2812d3133c4af185558af2733': class PDFImageXObject 17 0 obj d eae dx = Integrating the exponential function, of course, has the opposite effect: it divides by the constant in the exponent: 1 edx e ax ax , a /FlateDecode ] Exponential functions can be integrated, and you can test your ability to do so with this quiz and worksheet combo. /Width 1020 >> stream /Type /XObject /ColorSpace /DeviceRGB endobj Calc. /Type /XObject Anal. stream endobj /FlateDecode ] << /BitsPerComponent 8 /FlateDecode ] /Width 1283 >> % 'FormXob.39fed13b54d6df9e6ff552768a41b9e5': class PDFImageXObject /Subtype /Link endobj << /BitsPerComponent 8 /Height 93 /Subtype /Image The exponential integrals , , , , , , and are defined for all complex values of the parameter and the variable .The function is an analytical functions of and over the whole complex ‐ and ‐planes excluding the branch cut on the ‐plane. �}^�p��w�{��y� stream << /F1+0 70 0 R /FormXob.4caa680fc779b56803f6127fe3f16f9f 21 0 R /Width 630 >> /Filter [ /ASCII85Decode /FormXob.dce2fe057584215fb743584ad2229fb1 22 0 R /Width 1293 >> endobj /Length 7806 )Sdtq"I!7(#Uo/!8u0Wn.2endstream /FormXob.714905f6842e063ca4ffcc2eec80bee2 16 0 R /FlateDecode ] /Type /XObject /Type /XObject /FlateDecode ] 19 0 obj % 'FormXob.706a4adf6192e00b64f6556e0a16ed22': class PDFImageXObject /Subtype /Image Such a function is called an exponential function. /FormXob.6b55703c672f52a33c5d64d8ba7d1bb0 8 0 R "Lj89#.k?6^~>endstream % 'FormXob.f41b62a04397ad4481fe1f06a74ba49e': class PDFImageXObject /FormXob.b1efc86d94e5bcf517ee6576c537d13b 7 0 R /ColorSpace /DeviceRGB << /BitsPerComponent 8 endobj We’ve shown that differentiating the exponential function just multiplies it by the constant in the exponent, that is to say, d d x e a x = a e a x. /FormXob.39fed13b54d6df9e6ff552768a41b9e5 10 0 R We will assume knowledge of the following well-known differentiation formulas : , where , and , where a is any positive constant not equal to 1 and is the natural (base e) logarithm of a. /Length 4026 /Height 100 /Width 423 >> 20 0 obj Applications of the Complex Exponential Integral By Murían S. Corrington 1. /Contents 88 0 R /Filter [ /ASCII85Decode Gb"0TgMS8ep5:s,V&W1aPR^"3/uJ11-IplC"4E!65h.#7j,&\rl17"?cfi;2d(E.DS?"TV@.JI_nr!!Nu0O';U7Jd?PLqrQU#=RLi/H?8N5m2)\!oS#s6f>sQ!"MLb"E%ItE!uB',E%^1ruVZ%^R*q^QeKoNDN'1WMcAC/a%AAWC>Cm)!gi.cI9W8.&c!.ABf!T-9aCe4a#rr-J^DEQ&!dN^66,q]MsN/Aq)3MP7]^eR#ME^>?+&cf=hP\o8m8n0B&HGR@n:GTQj;2pW>O%/%9F:GIKLR^3gs"0%jp6b2/[R2_lbo(9j2F*e4-kBCuYC7EPUOg)OmM6\KY1f^5Mtq&INg>%(E4;U2D,FjtF8fF@+;*6h:r+f+C);(,hGa*("%>,#t@OF%s/mkrBdA6Gr,EM:eXk?"SOtr/#L=D*sSF)aL6Ed)dU2F"PnqAsf^sFD:Fm6pApI]NAEjhMrAA;"\O#/L2U3*]lIn^EM#K[o_+5kTNr2eRI-FI6EesA_CY\UQ(5Kb_[[)lK"d-u_nSAiN"Zr1BCPC>Wl&.s^_tD._._94\X(#od18)qA%%#2.^MuJ(epT2e*%/On]k]aSn@k3#Q?)0Ar[s4hQMatA6*ll9csH(8c=W:]f@P^+)4qJ4O#J\t7BHia-qNSQ5cBL@us2?bBgI,)%#o/'rWY\BIuqN,],\X'>8gStS&ac:M99elaj,]1(cctkrKnICf_GUD2pe0Be^\Tcg*kpNfrf3oGWU+1tr->FV=Upq)GI?O%/n.c7E/=+/s!XY,1HQ=5+L1q0mHIcrkdY%;:L]=i.jcMc/ZIr!oA8F5ggh]smIVK-:\VLd*p2,m,P-/%6SXnD;rf4mVikZ!Tj[LI$$qNbDT+L_T)Ibp_+38-/8m2%.HkoD4jM2(YfqeQ+5O5WI$;.1;Nc&:lK>$K+V5IGbL"!]U-+"2+^J-0f]JJ+:N3"Q6*-ug\d"&TV\&siYZ&/QE:.IRFa#C$],4TqcApO^!Z]EnRW9R[u/e7A+>\]q.XGL$;fa%UHiEcVlZ3#&XJ? /FormXob.cb203efccdde3cf25c323216122a748d 15 0 R /Length 7021 /ImageI ] /Type /Page >> 6 0 R /ImageI ] It is ( ) . /Length 3402 /Height 97 Doceri is free in the iTunes app store. endobj 23 0 obj 5 0 R % 'FormXob.de0bacdce49b01a092576fb42ea2758a': class PDFImageXObject Exponential functions occur frequently in physical sciences, so it can be very helpful to be able to integrate them. !30(8i@zzzzz!+=0'\ZH!o~>endstream Gb"0Td?<6,%#&-)s$LFFOdStqJ.Mp'_K8f:/DH3@eL7-)o?06IPXgtH7C+=M8GO.%:AU2,]h$cGJUNA3$s(XY+[\3O:ef,3NLE=lJLbR0"mH7^j(&/sf@42bWC/-Dh'sI#MObiQfP]#$E7%V)u2+Jk5:X?&H)O/=FGIHX)7%"cieUgUDTACID,8"KlaXp]f[CZq#?^pJH!*/TKepL.8b.,fk7*a1#Ru$VXFAX.[?JZp5m5$A*AT9,_6Z:8S=['[6rpDuKf\X"42')0/0gUe[W5u7!qtaf3iD5;gJ5kKoGga.[FHcdUAV(!;-rU8QQrYI0:og;6]7Ec_FCE^\)8hla7hBNpptA^@gCG2mHVL;sopP]>Z'j),Zfa(?O,Bh>)V4>'g(Gc3u]No4ML6k?.=fshTRQD_-:iLp_f3eA;F6uRMJ(=?[QU:Q&Zd(7.k*W2uAX)oRiT$rRqc%7=JD:rnoI#-h7X5j18@;-r+J;AKLAhL#p:dPS*l%F_e,W$_Q$R@kSNNU-2EWk=_nL9g-/3V2@L*QnuT7;?]PT(7]:2!q0/?Z2oCVbd8)@sWm;MBk:qbU,@0,3G"9$8?er#$Y'S[Vl;R8d&dCIpdZPS[^TX>X/T7d6at8S?1e2P7FYg8Qo!NYR](b0IZ')AGdW7d=l3B/X/\'mGpRTkH?gg,,/FDDi)7*p99b>_PCrSnhUZs#I+q9iTYI^'$QBBf*ZlXK9O>H";]\N>\9"[#lonE_#+f^N(>(_DD)kbK4V3P&DCk*]S&36[7GrN_HUGrN1AXOK%6!O2LajP]rI\IKag9>_M3,j'D_!pX1>]j/M'gQc#s8SNl@Vcb?7haSrasXbC!?JnE][^a)Im8^+GV8L!\t+="I(Vfm5([^'%"[d^sA["Li+WYUjWI-!hj=Ho:n-KurVc@9aq^m]9f$/4B.B=#[gRruuBM,t)'V2=WHEPY">OJ00f8/"3ni*'),8)JYLk]M1)=R,mpC^:B">qtc]&-o.(N8q%(;S,$WEIJ^eJrVn7hus,dk9$No;rZN>[6mr2Z8!0HS70! 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