Arclength is the of a section of a differentiable curve. Finding the length of an arc is useful in many applications, for the length of a curve can represent distance traveled, work, etc. It is commonly represented as or the differential if one is differentiating or integrating with respect to change in arclength.
This formula is derived by viewing arclength as the Riemann sum
The term being summed is the length of an approximating secant to the curve over the distance . As vanishes, the sum approaches the arclength, as desired. Arclength can also be derived for polar coordinates from the general formula for vector functions given above. The result is
|Date of creation||2013-03-22 12:02:43|
|Last modified on||2013-03-22 12:02:43|
|Last modified by||mathcam (2727)|
|Synonym||length of a curve|