Chapter 10, Problem 54RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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=7cosÎ¸, y=7sinÎ¸

Interval: 0â‰¤Î¸â‰¤Ï€

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 aâ‰¤tâ‰¤b (except possibly at the end points), then the arc length of C over the interval is given by

s=âˆ«ab(dxdt)2+(dydt)2dt

Consider the given parametric equations,

x=7cosÎ¸, y=7sinÎ¸

Now,

dxdÎ¸=ddÎ¸(7cosÎ¸)=âˆ’7sinÎ¸

And,

dydÎ¸=ddÎ¸(7sinÎ¸)=7cosÎ¸

Then, the arc length of the curve over the interval 0â‰¤Î¸"

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