# mth.122.handout.10 - MTH 122 Calculus II Essex County...

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MTH 122 — Calculus IIEssex County College — Division of Mathematics and Physics1Lecture Notes #10 — Sakai Web Project Material1Arc LengthEveryone should be familiar with the distance formula that was introduced in elementary algebra.It is a basic formula for the linear distance between two points in the plane. It states that thedistance between (x1, y1) and (x2, y2) isd=q(x2-x1)2+ (y2-y1)2.This distance, of course, is for a line connecting those two points. However, what if we have acurve and we want to know the distance along that curve between two points? We will basicallycut the curve into an infinite number of small linear sections, and then add these sections togetherto get the arc length, or distance between two points on the curve. Here a definite integral canbe used to find the arc length, where we have a curve,f(x), and two points on this curve thatare connected by a curve that is continuously differentiable on the interval.Arc Length Formula:Iff0is continuous on [a, b], then the length of the curvey=f(x),axb, isL=Zbaq1 + [f0(x)]2dx.This can also be written asL=Zbas1 +dydx2dx.

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