Given a function , determine the length of the curve (or arc) from the point () to the point (). This value is given by the formula:
>
|
|
| (3.1) |
When calling ArcLength with the plot output option, three curves are plotted:
1. The expression (in red by default),
2. The integrand (in blue by default),
3. The expression (in green by default)
and thus, the value of the green line at the point b is the total arc length of the curve.
>
|
|
In general, the resulting integrand is difficult to solve.
You can also computer arc length using the ArcLengthTutor command.
|
Simple Example Using Single Stepping
|
|
>
|
|
| (3.1.1) |
| (3.1.2) |
>
|
|
| (3.1.3) |
| (3.1.4) |
| (3.1.5) |
| (3.1.6) |
| (3.1.7) |
|
|
Advanced Example Using Hyperbolic Cosine
|
|
One special case is the hyperbolic cosine function, which is defined as:
For example, this function gives the shape of a wire hanging from two points.
>
|
|
In this special case, the length of the curve is equal to the integral of .
>
|
|
>
|
|
|