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Error Bounds

The accuracy delivered by these methods is seen in the following error bounds. (Recall that the error bound is a bound on the absolute value of the difference between the actual area under the curve and its estimated value.)

For n intervals we express the error between the actual and approximate area by tex2html_wrap_inline213 . From page 306 of the text we have:

Trapezoidal error: tex2html_wrap_inline215 , where M is the maximum of |f''(x)| on [a,b]

Simpson's error: tex2html_wrap_inline221 , where K is the maximum of |f''''(x)| on [a,b]

Sean O Anderson
Mon Nov 11 16:16:00 EST 1996