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Section 4.3 Indefinite Integrals and Net Change Theorem Math 1231: Single-Variable Calculus

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Indefinite Integrals Indefinite integral = anti-derivative

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Definite integral v.s. Indefinite integral Example A definite integral is a number; an indefinite integral is a function. The connection between them is given by

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Table of Indefinite Integrals

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Fundamental Theorem of Calculus: Part I The signed area function defined by f is an anti-derivative of f.

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Examples

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Applications: Net Change Theorem

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Differentiation and Integration: Inverse processes The Fundamental Theorem of Calculus If f is continuous on [a, b], then 1. : If f is integrated and then is differentiated, we arrive back to f. 2. : If we take a function F, first differentiate it then integrate it, we arrive back to F, but in the form of F(b) – F(a).

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Net Change Theorem: Examples

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More Examples

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