   Chapter 10, Problem 54RE

Chapter
Section
Textbook Problem

Arc Length In Exercises 53 and 54, find the arc length of the curve on the given interval.Parametric Equations Interval x = 7 cos θ ,   y =7sin θ 0 ≤ θ ≤ π

To determine

To calculate: The arc length of the curve x=7cosθ, y=7sinθ on the given interval 0θπ.

Explanation

Given: Parametric equations: x=7cosθ, y=7sinθ

Interval: 0θπ

Calculation: If a smooth curve C is given by x=f(t) and y=g(t) such that C does not intersect itself on the interval atb (except possibly at the end points), then the arc length of C over the interval is given by

s=ab(dxdt)2+(dydt)2dt

Consider the given parametric equations,

x=7cosθ, y=7sinθ

Now,

dxdθ=ddθ(7cosθ)=7sinθ

And,

dydθ=ddθ(7sinθ)=7cosθ

Then, the arc length of the curve over the interval 0θ"

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