   Chapter 10.3, Problem 46E

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 = 6 t 2 , y = 2 t 3 1 ≤ t ≤ 4

To determine

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

Explanation

Given:

The parametric equations,

x=6t2y=2t3

And, the interval 1t4.

Formula used:

Arc length of Curve is given by:

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

Calculation:

Consider the parametric equations,

x=6t2y=2t3

Differentiate x=6t2 with respect to t, to get,

dxdt=12t

Differentiate y=2t3 with respect to t, to get,

dydt=6t2

Arc length of Curve is given by:

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

Substitute the values of dxdt and dydt in above equation, to get,

s=14((12t)2+(6t2)2)dt=14144t2+36t2dt=1436t2(1+4t2)dt=614t(1+4t2)dt

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