Can someone please help me prove this? I've tried it to work it out in different ways and I'm beat. Will appreciate your help.
The problem reads:
Let be a continuous function on . The length of the curve on the interval is defined by
(don't know how to the _P under the sup)
and the supremum is taken over all partition points of .
Assume that has continuous derivative on . Take any partition of and derive
Next, use the Mean Value Theorem, and then use the definition of the Reimann integral to establish that
Thank you so much for your help.