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	<id>https://mathresearch.utsa.edu/wiki/index.php?action=history&amp;feed=atom&amp;title=Accumulated_Change</id>
	<title>Accumulated Change - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://mathresearch.utsa.edu/wiki/index.php?action=history&amp;feed=atom&amp;title=Accumulated_Change"/>
	<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;action=history"/>
	<updated>2026-04-15T00:45:35Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.34.1</generator>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=3151&amp;oldid=prev</id>
		<title>Khanh: /* Licensing */</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=3151&amp;oldid=prev"/>
		<updated>2021-10-28T20:57:47Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Licensing&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:57, 28 October 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l172&quot; &gt;Line 172:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 172:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Licensing==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Licensing==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Content obtained and/or adapted from:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Content obtained and/or adapted from:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[https://en.wikipedia.org/wiki/Riemann_sum Riemann sum, Wikipedia] under a CC BY-SA license&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;*&lt;/ins&gt;[https://en.wikipedia.org/wiki/Riemann_sum Riemann sum, Wikipedia] under a CC BY-SA license&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=3149&amp;oldid=prev</id>
		<title>Khanh at 20:53, 28 October 2021</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=3149&amp;oldid=prev"/>
		<updated>2021-10-28T20:53:49Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:53, 28 October 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l169&quot; &gt;Line 169:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 169:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Ostebee, Arnold; Zorn, Paul (2002). Calculus from Graphical, Numerical, and Symbolic Points of View (Second ed.). p. M-34. We chop the plane region R into m smaller regions R1, R2, R3, ..., Rm, perhaps of different sizes and shapes. The 'size' of a subregion Ri is now taken to be its area, denoted by ΔAi.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Ostebee, Arnold; Zorn, Paul (2002). Calculus from Graphical, Numerical, and Symbolic Points of View (Second ed.). p. M-34. We chop the plane region R into m smaller regions R1, R2, R3, ..., Rm, perhaps of different sizes and shapes. The 'size' of a subregion Ri is now taken to be its area, denoted by ΔAi.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Swokowski, Earl W. (1979). Calculus with Analytic Geometry (Second ed.). Boston, MA: Prindle, Weber &amp;amp; Schmidt. pp. 857–858. ISBN 0-87150-268-2.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;# Swokowski, Earl W. (1979). Calculus with Analytic Geometry (Second ed.). Boston, MA: Prindle, Weber &amp;amp; Schmidt. pp. 857–858. ISBN 0-87150-268-2.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Licensing==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Content obtained and/or adapted from:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://en.wikipedia.org/wiki/Riemann_sum Riemann sum, Wikipedia] under a CC BY-SA license&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=2113&amp;oldid=prev</id>
		<title>Khanh at 06:02, 12 October 2021</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=2113&amp;oldid=prev"/>
		<updated>2021-10-12T06:02:50Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;a href=&quot;https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;amp;diff=2113&amp;amp;oldid=600&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=600&amp;oldid=prev</id>
		<title>Rylee.taylor: added Accumulated Change powerpoint by professor Roberts</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Accumulated_Change&amp;diff=600&amp;oldid=prev"/>
		<updated>2020-08-18T00:33:06Z</updated>

		<summary type="html">&lt;p&gt;added Accumulated Change powerpoint by professor Roberts&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;* [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Accumulated%20Change/Presentation11_Distance_Definite_Integral.pptx Accumulated Change]. PowerPoint file created by Professor Cynthia Roberts, UTSA.&lt;/div&gt;</summary>
		<author><name>Rylee.taylor</name></author>
		
	</entry>
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