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A graphical approach to integration and the fundamental theorem

By David Tall


In ‘Understanding the Calculus’ 3 I suggested how the concepts of the calculus could be approached globally using moving computer graphics. The idea of area under a graph\ud presents a fundamentally greater problem than that of the notion of gradient. Each numerical gradient is found in a single calculation as a quotient f(x+h)-f(x)h but the calculation of the approximate area under a graph requires many intermediate calculations. Using algebraic methods the summation in all but the simplest examples becomes exceedingly difficult. A calculator initially allows easier numerical calculations but these can become tedious to carry out and obscure to interpret. Graduating to a computer\ud affords insight in two ways: through powerful number-crunching and dynamic graphical\ud display

Topics: QA
Publisher: Association of Teachers of Mathematics
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  1. (1985). A numerical approach to integration,
  2. (1986). Tall: Graphic Calculus II (Integration) for the BBC Computer, Glentop Publishers,
  3. (1985). Tall: The gradient of a graph,
  4. (1985). Tall: Understanding the calculus, doi
  5. (1982). Teaching Calculus (Blackie) doi

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