{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "
" -1 257 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" 
-1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 
0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 
0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "eq[1] := a + b + c + d = 1;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"\"/,*%\"aGF'%\"bGF'%\"cGF'%\"dGF'F'" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eq[2] := (1/3)*b + (2/3)*
c + d = 1/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"#/,(*&\"
\"$!\"\"%\"bG\"\"\"F.*(F'F.F+F,%\"cGF.F.%\"dGF.#F.F'" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 41 "eq[3] := (1/3)^2*b + (2/3)^2*c + d = 1/3;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"$/,(*&\"\"*!\"\"%\"bG
\"\"\"F.*(\"\"%F.F+F,%\"cGF.F.%\"dGF.#F.F'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 "eq[4] := (1/3)^3*b + (2/3)^3*c + d = 1/4;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"%/,(*&\"#F!\"\"%\"bG\"\"\"F.*(
\"\")F.F+F,%\"cGF.F.%\"dGF.#F.F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "solve(\{seq(eq[k],k=1..4)\},\{a,b,c,d\});" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#<&/%\"cG#\"\"$\"\")/%\"bGF&/%\"aG#\"\"\"F(/%
\"dGF-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 9 "Example 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eq[1] := s[1]+s[2] = 1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"\"/,&&%\"sGF&F'&F+6#\"\"#F'F'" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "eq[2] := s[1]*t[1]+s[2]*t
[2] = 1/2; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"#/,&*&&%\"
sG6#\"\"\"F.&%\"tGF-F.F.*&&F,F&F.&F0F&F.F.#F.F'" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 39 "eq[3] := s[1]*t[1]^2+s[2]*t[2]^2 = 1/3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"$/,&*&&%\"sG6#\"\"\"F.)&%
\"tGF-\"\"#F.F.*&&F,6#F2F.)&F1F5F2F.F.#F.F'" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 39 "eq[4] := s[1]*t[1]^3+s[2]*t[2]^3 = 1/4;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"%/,&*&&%\"sG6#\"\"\"F.)&%\"tGF-
\"\"$F.F.*&&F,6#\"\"#F.)&F1F5F2F.F.#F.F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "solve( \{seq(eq[k],k=1..4)\},\{s[1],s[2],t[1],t[2]\})
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/&%\"tG6#\"\"#-%'RootOfG6#,(*&
\"\"'\"\"\")%#_ZGF(F/F/*&F.F/F1F/!\"\"F/F//&%\"sGF'#F/F(/&F66#F/F7/&F&
F:,&F)F3F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "T := solve(
6*z^2-6*z+1=0,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG6$,&#\"\"\"
\"\"#F(*&\"\"'!\"\"\"\"$F'F(,&F'F(*&F+F,F-F'F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 25 "solve(6*z^2-6*z+1.0=0,z);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+Y8v')y!#5$\"
+a'[K6#F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "-T[1]+1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#\"\"\"\"\"#F%*&\"\"'!\"\"\"\"$F$F)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "-T[2]+1;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&#\"\"\"\"\"#F%*&\"\"'!\"\"\"\"$F$F%" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "Estimate \+
the order of error on Simpson's rules" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "for k from 0 to 5 do\n
   f := x^k:  # test polynomial\n   err := int(f,x=0..h)-\n         (h
/6)*(subs(x=0,f)+4*subs(x=h/2,f)+subs(x=h,f)):\n   print(f, err):\nend
 do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$%\"xG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"x
G\"\"#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"$\"\"
\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"%\"\"\",$*&\"$?
\"!\"\"%\"hG\"\"&F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"&\"
\"\",$*&\"#[!\"\"%\"hG\"\"'F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 45 "Thereofore, the error for Simpson's r
ule is  " }{XPPEDIT 18 0 "O(h^5);" "6#-%\"OG6#*$%\"hG\"\"&" }{TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "Fo
r Simpson's three-eighth rule:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "for k from 0 to 5 do\n   f \+
:= x^k:  # test polynomial\n   err := int(f,x=0..h)-\n         (h/8)*(
subs(x=0,f)+3*subs(x=h/3,f)+\n                3*subs(x=2*h/3,f)+subs(x
=h,f)):\n   print(f, err):\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"#\"\"\"\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$*$)%\"xG\"\"$\"\"\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$*$)%\"xG\"\"%\"\"\",$*&\"$q#!\"\"%\"hG\"\"&F+" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"&\"\"\",$*&\"$3\"!\"\"%\"hG\"\"'
F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "The error is  " }{XPPEDIT 
18 0 "O(h^5);" "6#-%\"OG6#*$%\"hG\"\"&" }{TEXT -1 44 ".  No apparent a
dvantage over Simpson's rule" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "On Trapezoidal \+
rule:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 145 "for k from 0 to 3 do\n   f := x^k:  # test polynomia
l\n   err := int(f,x=0..h)-\n         (h/2)*(subs(x=0,f)+subs(x=h,f)):
\n   print(f, err):\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$*$)%\"xG\"\"#\"\"\",$*&\"\"'!\"\"%\"hG\"\"$F+" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"xG\"\"$\"\"\",$*&\"\"%!\"\"%\"hG
F*F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 9 "Error is " }{XPPEDIT 18 0 "O(h^3);" "6#-%\"OG6#*$%\"hG\"\"$" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 206 "t1 := 1/2 + sqrt(3)/6:  t2 := 1/2-sqrt(3)/6:\nf
or k from 0 to 5 do\n   f := x^k:  # test polynomial\n   err := int(f,
x=0..h)-\n         (h/2)*(subs(x=h*t1,f)+subs(x=h*t2,f)):\n   print(f,
 simplify(err)):\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$*$)%\"xG\"\"#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$*$)%\"xG\"\"$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%
\"xG\"\"%\"\"\",$*&\"$!=!\"\"%\"hG\"\"&F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$*$)%\"xG\"\"&\"\"\",$*&\"#s!\"\"%\"hG\"\"'F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "Th
e error is  " }{XPPEDIT 18 0 "O(h^5);" "6#-%\"OG6#*$%\"hG\"\"&" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Composite numerical integ
ration program" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 256 976 "Compos
iteIntegral := proc(  f :: algebraic,\n                            t :
: name,\n                            a :: numeric,\n                  \+
          b :: numeric,\n                            n :: integer,\n  \+
                       rule :: procedure\n                          )
\n   local h, x, s, k;\n  \n   h := evalf( (b-a)/n );\n   x[0] := a;\n
   for k from 1 to n do\n      x[k] := a + k*h;\n   end do;\n\n   s :=
 0;  \n   for k from 1 to n do\n      s := s + rule(f,t,x[k-1],x[k]);
\n   end do;\n\n   return s;\nend proc;\n\nSimpson := proc(  f :: alge
braic,\n                  t :: name,\n                  a :: numeric,
\n                  b :: numeric\n                        )\n   return
 evalf((b-a)*(subs(t=a,f)+4*subs(t=(a+b)/2,f)+\n                      \+
subs(t=b,f))/6)\nend proc;\n\nTrap := proc(   f :: algebraic,\n       \+
         t :: name,\n                a :: numeric,\n                b \+
:: numeric\n                        )\n   return evalf((b-a)*(subs(t=a
,f)+subs(t=b,f))/2)\nend proc;\n" }{TEXT -1 1 "\n" }{TEXT 257 328 "gau
ss := proc(  f :: algebraic,\n                t :: name,\n            \+
    a :: numeric,\n                b :: numeric\n                     \+
   )\n   local t1, t2;\n  \n   t1, t2 := 1/2 + sqrt(3)/6, 1/2-sqrt(3)/
6;\n   return evalf((b-a)*(subs(t=(b-a)*t1+a,f)\n                     \+
 +subs(t=(b-a)*t2+a,f))/2)\nend proc;                  " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "read \"c:/304/compint.txt\":" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f := 3*cos(t)-ln(t);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&\"\"$\"\"\"-%$cosG6#%\"tGF(F
(-%#lnGF+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Composite
Integral(f,t,1,3,10,Simpson);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+5*
*)oR$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "CompositeInteg
ral(f,t,1,3,10,gauss);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+?(*)oR$!
\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h := (3-1)/10; evalf
(h^5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG#\"\"\"\"\"&" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+++++K!#8" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "evalf(int(f,t=1..3));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$!+(z*)oR$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Com
positeIntegral(f,t,1,3,10,Trap);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!
+@Om(Q$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(h^3);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++!)!#7" }}}{EXCHG {PARA 11 
"" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Com
positeIntegral(f,t,1,3,100,Trap);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
!+Rvz'R$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK 
"24 7 1" 915 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 
1 1 }