What kinds of problems are we looking at in this section?
Calculating the linear length of a curve (arc length -- and
then we'll use that in the next section, surface area
calculations for areas of revolution).
Let's start with arc length:
The usual trick is to discretize something continuous, and then pass to a limit:
Now hopefully we can figure out how the formula will look:
So what's the general formula?
Examples:
#37, p. 568
#3, p. 567
#25
#21
Links:
Here's
a nice summary of Numerical Integration, focused on the use of Mathematica to
illustrate them. Interesting even if you don't use Mathematica. By the
way, the Mathematica code used is antique, and needs to be brought into the
modern world....
Website maintained by Andy Long.
Comments appreciated.