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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Chapter
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.

39. x = t − 2 sin t, y = 1 − 2 cos t, 0 ≤ t ≤ 4π

To determine

To find: The length of the curve for the parametric equation x=t2sint and y=12cost .

Explanation

Given:

The parametric equation for the variable x is as below.

x=t2sint

The parametric equation for the variable y is as below.

y=12cost

Calculation:

The length of the curve is obtained by.

L=αβ(dxdt)2+(dydt)2dt

Differentiate the variable x with respect to t .

x=t2sintdxdt=12cost

Differentiate the variable y with respect to t :

y=12costdydt=2sint

Write the parametric equation of the curve.

Use the parametric equation for the variable x as below.

x=f(t)

Use the parametric equation for the variable y as below.

y=g(t)

The limit for the variable t will range from α to β .

Write the length of the curve formula

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th