Tall, David. (1986) A graphical approach to integration and the fundamental theorem. Mathematics Teaching, Vol.11 . pp. 48-51. ISSN 0025-5785

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Abstract

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 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 affords insight in two ways: through powerful number-crunching and dynamic graphical display.

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