I am in complete agreement that technology renders a number of previously core topics irrelevant, but I would not put Simpson's rule on this list.
The following is a question I included on my most recent AB Calculus test illustrating the importance of numerical integration methods. Most calculus curriculums (including the AP exam) ignore the application of calculus to discrete numerical data. Paul Foerster's calculus book (Key Curriculum Press) does an outstanding job of incorporating numerical work within an AP curriculum.
3. The following table lists the estimated rate of increase in the European-extraction population of Pennsylvania from 1700 to 1740.
a. Estimate the increase in the European-extraction population of Pennsylvania from 1700 to 1740 using the Trapezoid method. b. Find a new estimate using Simpson's Rule. c. Which answer is more reliable? Why?
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