Finding the
arc length of a function on an interval is another
application of the
definite integral.
Everyone knows the
distance formula, sqrt((x
2-x
1)^2 + (y
2-y
1)^2), but that only works for straight lines formed from connecting two points. The equation for finding
arc length is simple, but taking the
integral of the equation may be extremely difficult. In short, get a
graphing calculator that can calculate integrals, or get math software (
Derive,
Mathematica, etc.) for the same purpose.
Enough rambling. The equation to find arc length is Sab sqrt(1 + (dy/dx)^2)dx. If you find it difficult or impossible to find the integral in this manner, try Scd sqrt(1 + (dx/dy)^2)dy. Both of these equations assume that their functions are differentiable on the intervals [a,b] and [c,d], respectively.