Line Integrals of Scalar Functions

Accumulating a scalar quantity such as mass density along a curve, integrating against arc length rather than against a field's direction.

Active Calculus Multivariable, Line Integrals of Scalar Functions

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2 exercises

Activity 13.6.4

In this activity, we will be explaining each of the Properties from Properties of Scalar Line Integrals in the context of our copium mining analogy from this activity. Remember that the curve in our scalar line integral corresponds to the path the mining rig will take and the function in the scalar line integral measures the density of copium at that point on the surface.

Explain in your own words…

2.5

Exercise 15

Calculate the following line integral where $C$ is the path on $x=y$ with $-1 \geq y \geq 2$ :

2.5

Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.