The Fundamental Theorem of Calculus

Thomas J. Pfaff ()
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Thomas J. Pfaff: Ithaca College, Department of Mathematics

Chapter Chapter 30 in Applied Calculus with R, 2023, pp 349-358 from Springer

Abstract: Abstract From Chapter 29 we recognize that there is a relationship between the accumulation function and the derivative. Specifically, if we start with the graph of f(x) and sketch its accumulation function A(x) then the slope or derivative graph of A(x) is just f(x) again. This relationship is formalized with The Fundamental Theorem of Calculus given in M-Box 30.1. Note that the starting point, given by a in the formula, is not specified. In fact, any a will do as the effect of a is to simply shift A(x) up or down. Shifting a function up or down does not change its derivative.

Date: 2023
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DOI: 10.1007/978-3-031-28571-4_30

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