(*^
::[ Information =
"This is a Mathematica Notebook file. It contains ASCII text, and can be
transferred by email, ftp, or other text-file transfer utility. It should
be read or edited using a copy of Mathematica or MathReader. If you
received this as email, use your mail application or copy/paste to save
everything from the line containing (*^ down to the line containing ^*)
into a plain text file. On some systems you may have to give the file a
name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
The line below identifies what version of Mathematica created this file,
but it can be opened using any other version as well.";
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MacintoshStandardFontEncoding;
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fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times";
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fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times";
fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
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fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier";
fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier";
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fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier";
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ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Graphics`Graphics`"];
pol[i_,n_]:= Graphics[{GrayLevel[0.65],Polygon[{{(i-1)/n,0},
{i/n,0},
{i/n,(i/n)^2},
{(i-1)/n,((i-1)/n)^2}}]}];
vert[i_,n_]:= Graphics[{Dashing[{0.01,0.01}],Line[{{i/n,0},{i/n,(i/n)^2}}]}];
partit[n_]:= Show[Table[vert[i,n],{i,1,n}]];
pict[n_]:= Show[Table[pol[i,n],{i,1,n}],
Plot[t^2,{t,0,1}], partit[n],
PlotRange->{{0,1.05},{0,1.05}},
PlotLabel -> "n ="OutputForm[n],
Axes->True,
AxesLabel->{"x","y"},
Ticks->{{{1,"t"}},{0}}];
Show[GraphicsArray[{{pict[1],pict[2]},
{pict[3],pict[4]},
{pict[5],pict[6]}}],PlotLabel->"Figure 10.3\n y = g(x)"]
^*)