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{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 }