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The Fundamental Theorem of Calculus

In: Applied Calculus with R

Author

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  • Thomas J. Pfaff

    (Ithaca College, Department of Mathematics)

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.

Suggested Citation

  • Thomas J. Pfaff, 2023. "The Fundamental Theorem of Calculus," Springer Books, in: Applied Calculus with R, chapter 0, pages 349-358, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28571-4_30
    DOI: 10.1007/978-3-031-28571-4_30
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