   Chapter 10.2, Problem 40E

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.40. x = t + t , y = t − t , 0 ≤ t ≤ 1

To determine

To find: The length of the curve for the parametric equation x=t+t and y=tt.

Explanation

Given:

The parametric equation for the variable x is x=t+t.

The parametric equation for the variable y is y=tt.

Calculation:

The length of the curve is obtained by the below formula.

L=αβ(dxdt)2+(dydt)2dt

Differentiate the variable x with respect to t.

x=t+tdxdt=1+12t

Differentiate the variable y with respect to t:

y=1tdydt=112t

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.

L=αβ(dxdt)2+(dydt)2dt

Substitute (1+12t) for dxdt and (112t) for dydt in the above equation

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