Lengths of Curves

When finding the length of a given curve, divide the curve up into very small segments and calculate the length of each segment.  Add up the lengths found.

Measure the intervals by keeping the Dx the same for each interval.  Each segment approximates a straight line, so use the distance formula to find the length of each segment.


The length of the curve will be approximated by .  Simplifying,

 THEOREM
If a smooth curve begins at (a,c) and ends at (b,d), then the arc length of the curve  is given by


 or


 
 


Problems