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 . From page 306 of the text we have:

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

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

Mon Nov 11 16:16:00 EST 1996