{VERSION 2 3 "APPLE_68K_MAC" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 116 111 127 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 112 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 150 0 172 0 0 0 0 0 0 0 0 0 0 }1 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 104 168 230 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 " " 0 1 197 191 130 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 } } {SECT 0 {EXCHG {PARA 18 "" 0 "top_s07_2" {TEXT -1 45 "7.2 The Computa tion of the Definite Integral" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Bel monte, Summer 1996" }}{PARA 0 "" 0 "" {TEXT -1 119 "These are the shad ed gray examples which appear in Section 7.2. In-line plots have been \+ removed to conserve disk space." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "restart; f:=x->x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG: 6#%\"xG6\"6$%)operatorG%&arrowGF(*$9$\"\"#F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "dx:=(b - a) / n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dxG*&,&%\"bG\"\"\"%\"aG!\"\"F(%\"nGF*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "Sum(f(a + i*dx) * dx, i=1..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*(,&%\"aG\"\"\"*(%\"iGF),&%\"bGF)F(!\"\"F )%\"nGF.F)\"\"#F,F)F/F./F+;F)F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "area:=Sum(f(a + i*dx) * dx, i=1..n); value(\");" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%areaG-%$SumG6$*(,&%\"aG\"\"\"*(%\"iGF+,&%\"bG F+F*!\"\"F+%\"nGF0F+\"\"#F.F+F1F0/F-;F+F1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,N**%\"aG\"\"#%\"nG!\"\",&F'\"\"\"F*F*F*%\"bGF*F**(F%\" \"$F'F(F)F*F(**F%F*F'!\"#F+F&F)F&F***F%F*F'F/F+F&F)F*F(**F%F&F'F/F+F*F )F&F/**F%F&F'F/F+F*F)F*F&*(F%F-F'F/F)F&F**(F%F-F'F/F)F*F(*(F'!\"$F+F-F )F-#F*F-*(F'F6F+F-F)F&#F(F&*(F'F6F+F-F)F*#F*\"\"'**F'F6F+F&F%F*F)F-F(* *F'F6F+F&F%F*F)F&#F-F&**F'F6F+F&F%F*F)F*F9**F'F6F+F*F%F&F)F-F***F'F6F+ F*F%F&F)F&#F6F&**F'F6F+F*F%F&F)F*#F*F&*(F'F6F%F-F)F-#F(F-*(F'F6F%F-F)F &FE*(F'F6F%F-F)F*#F(F<*(F%F&F'F(F+F*F(*&F%F-F'F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Limit(area, n=infinity); value(\");" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$-%$SumG6$*(,&%\"aG\"\"\"*(% \"iGF,,&%\"bGF,F+!\"\"F,%\"nGF1F,\"\"#F/F,F2F1/F.;F,F2/F2%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"aG\"\"$#!\"\"F&*$%\"bGF&#\"\" \"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Int(f(x), x=a..b); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*$%\"xG\"\"#/F';%\"aG%\"b G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Int(f(x), x=a..b); val ue(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*$%\"xG\"\"#/F';% \"aG%\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"aG\"\"$#!\"\"F&*$% \"bGF&#\"\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Int(f(x) , x); value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*$%\"xG\" \"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%\"xG\"\"$#\"\"\"F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Int(sqrt(x^5 + 1), x=1..2); \+ evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*$,&*$%\"xG\"\" &\"\"\"F+F+#F+\"\"#/F);F+F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+dV5 ZJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10 0 \+ 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }