ࡱ>  "+ !#$%&'()*,1-./023Root Entry F B=f=Workbook_VBA_PROJECT_CUR"ce=fVBAcef @\p Greg Vainberg Ba= ThisWorkbook=C08X@"1Arial1Arial1Arial1Arial1Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *      `  $  $    (!@@  (!@  (! @  ! @  @  `@  `@  `  $    ,@  ,@  @@  @   @  `@  `@ @ ` Sheet1oSheet2Sheet3'TrapNumericalIntegration`i 3The test function used in this demonstration is x^2The actual Integral of x^2 The numerical Integration of x^2 Start Point End PointIntegral # of Points<This is a demonstration of trapezoidal numerical integration  @    dMbP?_*+%MAcrobat DistillerS odLetterPRIV0''''(\KhC(EBDAeBook"d??U}  }  }  } m                           ' ( ) * * * +?@@?@@=%Q@ '#$$$ testFunctionB?@D@|?@@=%zGD@'#$$$ testFunctionB ?$@t@?$@@=%(\u@'#$$$ testFunctionB  ?$@ t@ ?$@4@= %(t@ '#$ $ $  testFunctionB  ?4@& Ԥ@  ?4@@= %Q0@ '#$ $ $  testFunctionB  ?4@& Ԥ@  ?4@4@= %aڤ@ '#$ $ $  testFunctionB !?"4@& #Ԥ@  $?$4@$I@= &nɔդ@'#$ $ $  testFunctionB  "":b>@  7 Sheet1 @ '  dMbP?_*+%" ?? 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U>@7 Sheet3 ThisWorkbook Sheet1 Sheet2 Sheet30 !"#$%&'()*+,-./123456789:;<=>?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxz{|}~'##xME (SLSS<N0{00020819-0000-0000-C000-000000000046}@(%H@0x*CxAttribute VB_Name = "ThisWorkbook" Bas0{00020P819-0C$0046} |GlobalSpacFalse dCreatablPredeclaIdTru BExposeTemplateDerivBustomizD2'#xME (SLSS<N0{00020820-0000-0000-C000-000000000046}@(%H@0x*CxAttribute VB_Name = "She@et1" Bast0{00020820- C$0046} |Global!SpacFalse dCreatablPre declaIdTru BExposeTemplateDeriv$Bustom izD2'#xME (SLSS<N0{00020820-0000-0000-C000-000000000046}@(%H@0x*CxAttribute VB_Name = "She@et2" Bast0{00020820- C$0046} |Global!SpacFalse dCreatablPre declaIdTru BExposeTemplateDeriv$Bustom izD2'`#xME (SLSS<N0{00020820-0000-0000-C000-000000000046}@(%H@0x*CxAttribute VB_Name = "She@et3" Bast0{00020820- C$0046} |Global!SpacFalse dCreatablPre declaIdTru BExposeTemplateDeriv$Bustom izD2Module1 @__SRP_2y__SRP_3_VBA_PROJECT  B .xME (6 L<0%  ``<+x I" `8H`@l p(8\ @L < @, (  8 @ @ @ @@ (@ @ @ @| @l @\ @L @< @, @ @ @ @ @ @ @ @ @ @ @| @l @\ @L @< `(,  @ PX`  ( @ h  (x`(@ V`H  I. I0 I2 iZ@ l P(<J<@x\ @L @< 8`x*C$*\Rffff*22432a1f7f*\R1*#c4*\R1*#229B  B   0    ,8 H \P (x8ip " "' `iP 0 .  2'< 0V-------------------------------------------------------------------------------------- J Z 0$\ 'Jpx < J'V B 2 8 Z .$\'JFuncti J Z . < B $\ 'Jon yX-Attribute VB_Name = "Module1" Function test0(x)8 Pnx * x End2 T  TrapNumericalIntegra^(start, end&Points,LAs Sngdelta_x~(: - M) / G/ kBlRuln(T5,#For i1 To (,81F.ǁ*+ 22 + (f* i))NextU*('-RC$sH2/ 2)=E, rU~| iAX \L427ea778 Sheet3`H-Module122432a1f7fModule1.` x`0HL&L)DdNs_fM3ɴIX]fDEy.GAO[\!AqVL#VoMqA/24+TForTo Excel+ VBAWin16~Win32MacVBA6#Project1  stdole` VBAProject Officeu ThisWorkbook| _Evaluate Sheet1 Sheet2 Sheet3 Module1b (testFunctionC xo_B_var_FunctionO WorksheetWorkbookk MidPointRule6MPRNumericalIntegration^AstartIntendIntϗ NumPoints}deltaxC _B_var_deltax@delta_J _B_var_delta_@delta_xԚ_B_var_delta_xXstartIngi` _B_var_ForjL_B_var_i MsgBoxRIntegralɓ_B_var_IntegralRkstopIntz[ _B_var_ToInte\_B_var_stopInt}O(TrapNumericalIntegrationMPNumericalIntegrationE. 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