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

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Presentation transcript:

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

Indefinite Integrals Indefinite integral = anti-derivative

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

Table of Indefinite Integrals

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

Examples

Applications: Net Change Theorem

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).

Net Change Theorem: Examples

More Examples