   Chapter 10.3, Problem 51E

Chapter
Section
Textbook Problem

Arc Length In Exercises 49-54, find the arc length of the curve on the given interval.Parametric Equations Interval x = e − t cos t , y = e − t sin t 0 ≤ t ≤ π 2

To determine

To calculate: The arc length of curve x=etcost,y=etsint on the interval 0tπ2.

Explanation

Given:

The parametric equations,

x=etcosty=etsint

And, the interval 0tπ2.

Formula used:

Arc length of Curve is given by:

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

Calculation:

Consider the parametric equations,

x=etcosty=etsint

Differentiate x=etcost with respect to t, to get,

dxdt=et(sint)+cost(et)=etsintcostet=et(cost+sint)

Differentiate y=etsint with respect to t, to get,

dydt=et(cost)sint(et)=etcostsintet=et(costsint)

Arc length of Curve is given by:

s=

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