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{PARA 0 "" 0 "" {TEXT -1 180 "@ Copyright 1995-98 by Arlen Strader and
 Philip B. Yasskin, Texas A&M Univ.\n\nCalculus Demo: \n \n      Using
 Riemann Sums to Approximate the \n\n                    Area under a \+
Curve\n" }}{PARA 0 "" 0 "" {TEXT -1 119 "(You may need to edit the \"r
ead\" statement before executing.  It may need the full path to the fi
le inside the quotes.)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "with(stud
ent):   with(plots):\nread(\"riemann_init.m\");   INITIALIZE;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "This worked if the output says \"
" }{TEXT 256 16 "Demo Initialized" }{TEXT -1 61 ".\"  You need to fix \+
the \"read\" statement if the output says \"" }{TEXT 257 10 "INITIALIZ
E" }{TEXT -1 2 ".\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "\nDefine t
he function with which to work.  (A monotonic function is best.)\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f:=x->    ;   #e.g. x^2+9" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "\nDefine the ranges with which to \+
work and plot the function.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "xr
ange:=x=    ;   #e.g. 1..9\nyrange:=    ;   #e.g. 0..100" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(f(x),xrange,yrange);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "\nAnimate the Riemann sums\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "RightBox(f,xrange,8,color=maroon,sh
ading=blue);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "LeftBox(f,x
range,8,color=maroon,shading=red);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 65 "\nEvaluate Right Riemann sum for different numbers of rectangle
s.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "rightsum(f(x),xrange,1);\nv
alue(%)=evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 324 "value
(rightsum(f(x),xrange,8))=evalf(rightsum(f(x),xrange,8));\nvalue(right
sum(f(x),xrange,16))=evalf(rightsum(f(x),xrange,16));\nvalue(rightsum(
f(x),xrange,32))=evalf(rightsum(f(x),xrange,32));\nvalue(rightsum(f(x)
,xrange,64))=evalf(rightsum(f(x),xrange,64));\nvalue(rightsum(f(x),xra
nge,128))=evalf(rightsum(f(x),xrange,128));" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 25 "rightsum(f(x),xrange,n); " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "lim
it(%,n=infinity);   evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "
\nEvaluate Left Riemann sum for different numbers of rectangles.\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "leftsum(f(x),xrange,1);\nvalue(%)=e
valf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 314 "value(leftsum(
f(x),xrange,8))=evalf(leftsum(f(x),xrange,8));\nvalue(leftsum(f(x),xra
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))=evalf(leftsum(f(x),xrange,32));\nvalue(leftsum(f(x),xrange,64))=eva
lf(leftsum(f(x),xrange,64));\nvalue(leftsum(f(x),xrange,128))=evalf(le
ftsum(f(x),xrange,128));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 
"leftsum(f(x),xrange,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "
value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit(%,n=infinity);   ev
alf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "\nUse Integral to find
 area.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Int(f(x),xrange);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(f(x),xrange);   evalf(%)
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "\nUse Midpoints for Riemann \+
sum.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "MiddleBox(f,xrange,8,colo
r=maroon,shading=blue);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "
middlesum(f(x),xrange,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 
"value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit(%,n=infinity);   \+
evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "\nUse Trapezoids ins
tead of Rectangles.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "TrapBox(f,
xrange,8,color=maroon,shading=red);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "trapezoid(f(x),xrange,n);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit(%
,n=infinity);   evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "\nUs
e Simpson's Rule.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "simpson(f(x)
,xrange,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit(%,n=infinity);   evalf(%);" }
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