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	<title>Homework How-to &#187; trapezoid</title>
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		<title>Composite Figures</title>
		<link>http://homeworkhowto.com/composite-figures/</link>
		<comments>http://homeworkhowto.com/composite-figures/#comments</comments>
		<pubDate>Sat, 14 Nov 2009 00:35:23 +0000</pubDate>
		<dc:creator>Christine</dc:creator>
				<category><![CDATA[Geometry]]></category>
		<category><![CDATA[2D]]></category>
		<category><![CDATA[area]]></category>
		<category><![CDATA[composite]]></category>
		<category><![CDATA[different]]></category>
		<category><![CDATA[figure]]></category>
		<category><![CDATA[flat]]></category>
		<category><![CDATA[geometrical]]></category>
		<category><![CDATA[rectangle]]></category>
		<category><![CDATA[regular]]></category>
		<category><![CDATA[shape]]></category>
		<category><![CDATA[smaller]]></category>
		<category><![CDATA[split]]></category>
		<category><![CDATA[square]]></category>
		<category><![CDATA[trapezoid]]></category>
		<category><![CDATA[triangle]]></category>
		<category><![CDATA[volume]]></category>

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		<description><![CDATA[An Overview of Composite Figures Description A detailed tutorial on what composite figures are. Step by step tutorial including several examples of how to identify composite figures for reference. Overview A composite figure is any figure that can be split into more than one shape. Hardly any regular shapes are considered to be composite shapes. [...]]]></description>
			<content:encoded><![CDATA[<h3><strong>An Overview of Composite Figures</strong></h3>
<p><a href="http://homeworkhowto.com/composite-figures/"><em>Click here to view the embedded video.</em></a></p>
<hr /><strong></p>
<p class="content_description">Description</p>
<p></strong></p>
<p>A detailed tutorial on what composite figures are. Step by step tutorial including several examples of how to identify composite figures for reference.</p>
<p><strong></p>
<p class="content_overview">Overview</p>
<p></strong></p>
<p>A <strong>composite figure </strong>is any figure that can be split into more than one shape. Hardly any regular shapes are considered to be composite shapes. The only one is a regular trapezoid &#8211; it can be split into three shapes, two triangles and a rectangle. You could technically consider a rectangle to be a composite figure &#8211; you can split it into squares or smaller rectangles &#8211; but since it doesn&#8217;t need to be split into different shapes to solve for area, then it is not considered a composite figure.</p>
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		<title>Error Bounds: Trapezoidal Rule</title>
		<link>http://homeworkhowto.com/error-bounds-trapezoidal-rule/</link>
		<comments>http://homeworkhowto.com/error-bounds-trapezoidal-rule/#comments</comments>
		<pubDate>Fri, 25 Sep 2009 23:15:24 +0000</pubDate>
		<dc:creator>Christine</dc:creator>
				<category><![CDATA[Calculus]]></category>
		<category><![CDATA[definite integral]]></category>
		<category><![CDATA[error bound]]></category>
		<category><![CDATA[formula]]></category>
		<category><![CDATA[function]]></category>
		<category><![CDATA[graph]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[trapezium rule]]></category>
		<category><![CDATA[trapezoid]]></category>
		<category><![CDATA[trapezoid rule]]></category>
		<category><![CDATA[trapezoidal rule]]></category>

		<guid isPermaLink="false">http://homeworkhowto.com/error-bounds-trapezoidal-rule/</guid>
		<description><![CDATA[Using the Trapezoidal Rule to Solve Error Bounds Description     A detailed tutorial on using the trapezoidal rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the trapezoidal rule for reference.       Overview     The trapezoidal rule is a rule in calculus that is [...]]]></description>
			<content:encoded><![CDATA[<h3><strong>Using the Trapezoidal Rule to Solve Error Bounds</strong></h3>
<p><a href="http://homeworkhowto.com/error-bounds-trapezoidal-rule/"><em>Click here to view the embedded video.</em></a></p>
<hr /><strong></p>
<p class="content_description">Description</p>
<p> </p>
<p> </p>
<p></strong></p>
<p>A detailed tutorial on using the trapezoidal rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the trapezoidal rule for reference.</p>
<div><strong> </strong></div>
<p> </p>
<div><strong></strong></div>
<p> </p>
<p><strong></p>
<p class="content_overview">Overview</p>
<p> </p>
<p> </p>
<p></strong></p>
<p>The <strong>trapezoidal rule </strong>is a rule in calculus that is used to solve error bounds and evaluate the definite integral <img src='http://s.wordpress.com/latex.php?latex=%20%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29%5C%2Cdx.&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' \int_{a}^{b} f(x)\,dx.' title=' \int_{a}^{b} f(x)\,dx.' class='latex' /> The way that the trapezoidal rule works is that you take the region under a graph, approximate it as a trapezoid, and calculate the area. As a mathematical formula, this is the trapezoidal rule:</p>
<img src='http://s.wordpress.com/latex.php?latex=%20%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29%5C%2C%20dx%20%5Capprox%20%28b-a%29%5Cfrac%7Bf%28a%29%20%2B%20f%28b%29%7D%7B2%7D.&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' \int_{a}^{b} f(x)\, dx \approx (b-a)\frac{f(a) + f(b)}{2}.' title=' \int_{a}^{b} f(x)\, dx \approx (b-a)\frac{f(a) + f(b)}{2}.' class='latex' />
<p>The least complicated form of the trapezoidal rule is expressed as:</p>
<img src='http://s.wordpress.com/latex.php?latex=%20T%20%3D%20%5Ctfrac12%20%28b-a%29%20%28f%28a%29%2Bf%28b%29%29.%20&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt=' T = \tfrac12 (b-a) (f(a)+f(b)). ' title=' T = \tfrac12 (b-a) (f(a)+f(b)). ' class='latex' />
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