Formula for the Trapezoid RuleDate: 07/31/99 at 10:10:54 From: Lester J. Snyder Subject: The Trapezoid Rule I have searched on the Web, but cannot find the formula for the trapezoid rule. I also need to know how to use it. (I am writing a program to find the moment area of any shape.) Date: 08/01/99 at 22:58:12 From: Doctor Jaffee Subject: Re: The Trapezoid Rule To find an approximation for the integral of some function that is integrable from x(0) to x(n), divide the x-axis into equal parts and draw vertical segments from the endpoints of each part to a point on the curve. Connect those points and you will have n trapezoids whose total accumulation approximates the integral of the function for that interval. That is the idea behind the trapezoid rule. To use geometry to find the area of each trapezoid, add the total areas (keeping in mind that areas below the x-axis will have negative values). The result will be the width of the partition divided by 2 times f(x(0)) + 2f(x(1)) +2f(x(2)) + 2f(x(3)) + ... + 2f(x(n-1)) + f(x(n)), which is the formula for the trapezoid rule. An interesting Web page that illustrates this procedure can be found at: http://www.cs.utah.edu/~zachary/isp/applets/Integrate/Integrate.html Just follow the instructions (there is a useful help screen). - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ |
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