## Tutoring on Line Integrals

Learning Objectives:

#### Understand and Apply Line Integrals.

Math Tutoring on Line Integrals

One skill needed to successfully evaluate Line Integrals is to be able to define a smooth parameterization of a given path in the xy – plane. In math tutoring, this means we want to be able to break up a given curve and define it in terms of t so each piece is smooth while the value of ‘t’ remain continuous.

Fundamental Theorem of Line Integrals:

Let ‘C’ be a piecewise smooth curve lying in an open region R given by                             .

If ‘F’ is continuous, conservative vector field then,

Where ‘f’ is a potential function of ‘F’. That is .

Line Integrals in :

Let  be continuous in a region containing a smooth curve C. if C is given by

Line Integrals in :

Let  be continuous in a region containing a smooth curve C. if C is given by

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Hook Questions:

1.     What’s the skill needed to evaluate a Line Integrals?

2.     State the Fundamental Theorem of Line Integrals?

3.     State Line Integrals in .

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