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