   Chapter 10.2, Problem 39E

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.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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