{VERSION 2 3 "SGI IRIS UNIX" "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 0 0 0 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 } {CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "H eading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 256 21 "\nCalulus Worksheet V\n" }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 79 "In this worksheet we give a few e xamples how Maple can be\nused for integration:" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 28 "Integration by substitution:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=Int(x/sqrt(1-4*x^2),x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%\$IntG6\$*&%\"xG\"\"\",&F*F**\$F)\"\"#!\"%#!\"\"F- F)" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 255 "Calling Sequence:\n cha ngevar(s, f)\n changevar(s, f, u)\nParameters:\n s - an expression of the form h(x) = g(u), defining x as a function of u\n \+ f - an expression such as Int(F(x), x = a...b)\n u - the name of the new integration variable." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "changevar(1-4*x^2=u,A,u);Atemp:=value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\$IntG6\$,\$*\$%\"uG#!\"\"\"\"##F*\"\")F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&AtempG,\$*\$%\"uG#\"\"\"\"\"##!\"\"\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "subs(u=1-4*x^2,Atemp);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,\$*\$,&\"\"\"F&*\$%\"xG\"\"#!\"%#F&F)#! \"\"\"\"%" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 171 "Integration by p arts:\nCalling Sequence:\n intparts(f, u)\nParameters:\n f - an ex pression of the form Int(u*dv, x)\n u - the factor of the integrand \+ to be differentiated" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "B:=I nt(x*sin(x),x);Bparts:=intparts(B,x)=value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%\$IntG6\$*&%\"xG\"\"\"-%\$sinG6#F)F*F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'BpartsG/,&*&%\"xG\"\"\"-%\$cosG6#F(F)!\"\" -%\$IntG6\$,\$F*F-F(F-,&-%\$sinGF,F)F'F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "C:=Int(x^2*sin(x),x);Bparts:=intparts(C,x^2)=value(\" );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%\$IntG6\$*&%\"xG\"\"#-%\$si nG6#F)\"\"\"F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'BpartsG/,&*&%\"xG \"\"#-%\$cosG6#F(\"\"\"!\"\"-%\$IntG6\$,\$*&F(F-F*F-!\"#F(F.,(F'F.F*F)*&F( F--%\$sinGF,F-F)" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 " " 0 "" {TEXT -1 18 "Partial fractions:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "2/(x-1)-1/(x+2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, &*\$,&%\"xG\"\"\"!\"\"F'F(\"\"#*\$,&F&F'F)F'F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"\"\"&F&F&,&F%F&!\"\"F&F),&F%F&\"\"#F&F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "numer(\")/expand(denom(\"));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"\"\"&F&F&,(*\$F%\"\"#F&F %F&!\"#F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Int(\",x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\$IntG6\$*&,&%\"xG\"\"\"\"\"&F)F), (*\$F(\"\"#F)F(F)!\"#F)!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Int(2/(x-1)-1/(x+2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\$In tG6\$,&*\$,&%\"xG\"\"\"!\"\"F*F+\"\"#*\$,&F)F*F,F*F+F+F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "int(2/(x-1)-1/(x+2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#,&%\"xG\"\"\"!\"\"F)\"\"#-F%6#,&F( F)F+F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "convert((x+5)/( x^2+x-2),parfrac,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*\$,&%\"xG\" \"\"!\"\"F'F(\"\"#*\$,&F&F'F)F'F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Int((x^2-3*x+1)/(x^3+x^2-2*x),x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%\$IntG6\$*&,(*\$%\"xG\"\"#\"\"\"F)!\"\$F+F+F+,(*\$F)\"\" \$F+F(F+F)!\"#!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "par :=convert((x^2-3*x+1)/(x^3+x^2-2*x),parfrac,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\$parG,(*\$%\"xG!\"\"#F(\"\"#*\$,&F'\"\"\"F(F-F(#F(\"\"\$ *\$,&F'F-F*F-F(#\"#6\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Int(par,x);value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\$IntG6\$,(* \$%\"xG!\"\"#F)\"\"#*\$,&F(\"\"\"F)F.F)#F)\"\"\$*\$,&F(F.F+F.F)#\"#6\"\"'F (" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%#lnG6#%\"xG#!\"\"\"\"#-F%6#,& F'\"\"\"F)F.#F)\"\"\$-F%6#,&F'F.F*F.#\"#6\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "5 11 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 }