Transcription of Trapezoid Rule and Simpson’s Rule Trapezoid Rule y h h h x b
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Trapezoid Rule and Simpson’s Rule Trapezoid Rule y h h h x b
Trapezoid Rule and Simpson s Rulec 2002, 2008, 2010 Donald Kreider and Dwight LahrTrapezoid RuleMany applications of calculus involve definite integrals. If we can find an antiderivative for the integrand,then we can evaluate the integral fairly easily. When we cannot, we turn to numerical methods. Thenumerical method we will discuss here is called theTrapezoid Rule. Although we often can carry out thecalculations by hand, the method is most effective with the use of a computer or programmable at the moment let s not concern ourselves with these details. We will describe the method first, andthen consider ways to implement =x0x1x2x3 = by0y1y3hhhy2fThe general idea is to use trapezoids instead of rectangles to approximate the area under the graphof a function. A Trapezoid looks like a rectangle except that it has a slanted line for a top.
Trapezoid Rule and Simpson’s Rule c 2002, 2008, 2010 Donald Kreider and Dwight Lahr Trapezoid Rule Many applications of calculus involve de nite integrals. If we can nd an antiderivative for the integrand, then we can evaluate the integral fairly easily. When we cannot, we turn to numerical methods. The
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