on the interval
if the two following conditions are fulfilled:
is differentaible on
- The first derivative
is continuous on
is smooth, its graph is called a smooth curve
be a smooth function on the interval
. The length of the graph of
The length of an arc of parabola.
The length of the arc
is equal to:
Remark: To compute this integral, you can either use a table of integrals (for example http://torte.cs.berkeley.edu:90/tilu), or make an appropriate substitution. The example 5.20 can help you too.