9/11/2023 0 Comments Arc length calculus 2However, for calculating arc length we have a more stringent requirement for f(x). In previous applications of integration, we required the function f(x) to be integrable, or at most continuous. (The process is identical, with the roles of x and y reversed.) The techniques we use to find arc length can be extended to find the surface area of a surface of revolution, and we close the section with an examination of this concept.Īrc Length of the Curve y = f(x) We begin by calculating the arc length of curves defined as functions of x, then we examine the same process for curves defined as functions of y. Or, if a curve on a map represents a road, we might want to know how far we have to drive to reach our destination. If a rocket is launched along a parabolic path, we might want to know how far the rocket travels. Many real-world applications involve arc length. We can think of arc length as the distance you would travel if you were walking along the path of the curve. In this section, we use definite integrals to find the arc length of a curve.
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