   Chapter 10.3, Problem 48E

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 = arcsin t , y = ln 1 − t 2 0 ≤ t ≤ 1 2

To determine

To calculate: The arc length of curve x=3t+5,y=72t on the interval 1t3.

Explanation

Given:

The parametric equations,

x=arcsinty=ln1t2

And, the interval 0t12.

Formula used:

Arc length of Curve is given by:

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

Calculation:

Consider the parametric equations,

x=arcsinty=ln1t2

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

dxdt=11t2

Differentiate y=ln1t2 with respect to t, to get,

dydt=tt21

Arc length of curve is given by:

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

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