   Chapter 10.2, Problem 38E

Chapter
Section
Textbook Problem

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.38. x = t2 − t, y = t4, 1 ≤ t ≤ 4

To determine

To find: the length of the curve for the parametric equation x=t2t and y=t4 .

Explanation

Given:

The parametric equation for the variable x is as below.

x=t2t

The parametric equation for the variable y is as below.

y=t4

Calculation:

Differentiate the variable x with respect to t .

dxdt=2t1

Differentiate the variable y with respect to t :

dydt=4t3

The parametric equation for the variable x is as below.

x=f(t)

The parametric equation for the variable y is as below.

y=f(t)

The limit for the variable t ranges from α to β .

Write the length of the curve formula.

L=αβ(dxdt)2+(dydt)2dt

Substitute (2t1) for dxdt and (4t3) for dydt in the above equation

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