4Vector Integral Calculus

4.1 Line Integrals

In this section we will define and learn how to evaluate the line integrals of the form

(4.1)images

Before discussing the line integrals, however, let’s review the concept of indefinite and definite integrals.

4.1.1 Indefinite and Definite Integrals

We will first introduce the indefinite integral and then use it to present the definite integral.

Indefinite integral

The indefinite integral can be easily defined using the concept of a derivative as follows.

Consider a function f(x). If its integral exists, denoted,

(4.2)images

then

(4.3)images

Several useful integral formulas are presented next:

(4.4a)images
(4.4b)images
(4.4c)images
(4.4d)images
(4.4e)images
(4.4f)
(4.4g)
(4.4i)
(4.4j)
Definite Integral

If the indefinite ...

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