Rectification is the process of finding the length of an arc of a curve between two given points. The arc length formula uses the language of calculus to generalize and solve a classical problem in geometry : finding the length of a specific curve.



Given a function



The arc length formula uses the language of calculus to generalize and solve a classical problem in geometry : finding the length of a specific curve.Given a function that is defined and differentiable on the interval , the length L of the curve in that interval is



Curve : Let



Length of the curve: Let AB the curve defined by continuous function





Let Let be continuous function on . Then the graph of on i.e, is called a curve.Let AB the curve defined by continuous function on Let be the partition of into n equal parts each length h, where

Let



Let denote the sum of the length of segments of broken lines, then

1. Arc formula for cartesian equation

2. Length of an arc of a plan curve with parametric equation

3. Length of an arc of a plan curve with polar equation

1. If a function



If a function has continuous derivative on , then the length L of the arc of the curve from the point to the point is given by

If exist, then it is called length of the curve and is denoted by L. The number L, if exist, is unique.A continuous curve, which has length, is called rectifiable.The process of finding the length of an arc of a curve between two given points is called rectification.If C is curve defined by , where has a continuous derivative f'(x) an , then the length of the curve C is given byOrLet C is curve defined by parametric equation and , then length L of curve C is given by