   Chapter 10, Problem 53RE

Chapter
Section
Textbook Problem

# Arc Length In Exercises 53 and 54, find the arc length of the curse on the given interval.Parametric Equations Interval x = t 2 + 1 ,       y = 4 t 3 + 3 0 ≤ t ≤ 2

To determine

To calculate: The arc length of the curve of the parametric equation x=t2+1, y=4t3+3 on the provided interval 0t2.

Explanation

Given:

The provided parametric equation x=t2+1, y=4t3+3 and the interval is 0t2.

Formula Used:

Arc length can be calculated using the below formula:

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

Calculation:

A smooth curve C is represented as x=f(t) and y=g(t) such that C does not intersect itself at the interval atb except at the end points, then the arc length of curve and the interval is given as

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

Consider the provided parametric equations,

x=t2+1, y=4t3+3

So,

dxdt=ddt(t2+1)=2t

Then,

dydt=ddt(4t3+3)=12t2

Therefore, the arc length of the curve over the interval 0t2 is:

s=

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