The Idea of a Line Integral

Accumulating a vector field's push along an oriented curve — estimating from a picture whether the work done is positive, negative or zero.

Active Calculus Multivariable, The Idea of a Line Integral

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1 exercise

Activity 13.3.2

For each curve below, find a parametrization of the curve. Ensure that each curve's orientation matches the one specified.

The line segment in $\R^3$ from $(0,1,-2)$ to $(3,-1,2)$ .
The line segment in $\R^3$ from $(3,-1,2)$ to $(0,1,-2)$ .
The circle of radius $3$ (in $\R^2$ ) centered at the origin, beginning at the point $(0,-3)$ and proceeding clockwise around the circle.
In $\R^2$ , the portion of the parabola $y^2 = x$ from the point $(4,2)$ to the point $(1,-1)$ .

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.