Calculus_MA_224_Chapter_6_Section_3 - : Greater accuracy:...

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Calculus MA 224 Chapter 6 Section 3: Numerical Integration Approximation By Rectangles : If f(x) is positive on the interval axb, the definite integral f(x)dx is equal to the area under the graph of f between x=a and x=b. First, divide the interval axb into n equal subintervals of width and let x denote the beginning of the jth subinterval. Approximation by Trapezoids
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Unformatted text preview: : Greater accuracy: Area of a trapezoid = 1/2[f(x) +f(x+1)]x The sum of the areas of all n trapezoids is an approximation to the area under the curve and hence an approximation to the corresponding definite integral. Thus, = which is known as the Trapezoid Rule Accuracy of the Trapezoidal Rule : If M is the maximum value of on the interval axb, then...
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This note was uploaded on 04/12/2011 for the course MA 224 taught by Professor Swohead during the Winter '09 term at Purdue University-West Lafayette.

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