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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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 = t2t, 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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