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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 43 "t1, t2 := 1/2+sqrt(15)/10, 1/2-sqrt(15)/10;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%#t1G%#t2G6$,&#\"\"\"\"\"#F**&
\"#5!\"\"\"#:F)F*,&F)F**&F-F.F/F)F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 157 "for k from 0 to 6 do\n   f := x^k:\n   err := int(f,
x=0..h)-(h/18)*(5*subs(x=h*t1,f) + 5*subs(x=h*t2,f) + 8*subs(x=h/2,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\"\"$\"\"\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$*$)%\"xG\"\"%\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$*$)%\"xG\"\"&\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%
\"xG\"\"'\"\"\",$*&\"%+G!\"\"%\"hG\"\"(F'" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "Therefore, the accuracy o
f the formula is  " }{XPPEDIT 18 0 "O(h^7);" "6#-%\"OG6#*$)%\"hG\"\"(
\"\"\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 27 "The program for the formula" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 256 402 "newrule := p
roc(  f :: algebraic,\n                  x :: name,\n                 \+
 a :: numeric,\n                  b :: numeric )\n   local t1, t2, S1,
 S2, S3;\n\n   t1, t2 := evalf(1/2 + sqrt(15)/10), \n             eval
f(1/2 - sqrt(15)/10);\n   \n   S1 := evalf(subs(x=(b-a)*t1+a,f));\n   \+
S2 := evalf(subs(x=(b-a)*t2+a,f));\n   S3 := evalf(subs(x=(b+a)/2, f))
;\n\n   return ((b-a)/18)*(5*S1+5*S2+8*S3);\nend proc;" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "read \"c:/304/compint.txt\":
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "read \"c:/304/newrule.t
xt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f := 5*ln(x) + x^2
*cos(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&\"\"&\"\"\"-%#ln
G6#%\"xGF(F(*&)F,\"\"#F(-%$cosGF+F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "CompositeIntegral(f,x,1,3,6,newrule);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"+*)e$zG\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "evalf(int(f,x=1..3));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"+(yNzG\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
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