Arc length function
Definition
The arc length function calculates the total distance traveled along a curve between two points. It measures how much "length" there is on a curve rather than just measuring straight-line distances.
Analogy
Think of finding arc length as measuring how far you have walked while taking different paths in a park instead of just measuring straight-line distances from point A to point B.
Related terms
Tangent line: A straight line that touches a curve at only one point, representing the instantaneous direction of motion at that point.
Parametric equations: Equations that express the coordinates of a curve as functions of an independent parameter, often used to describe motion along a curve.
Riemann sum: An approximation method used in calculus to estimate the area under a curve or the length of a curve by dividing it into smaller parts.
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