   Chapter 10.2, Problem 37E

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.37. x = t + e−t, y = t − e−t, 0 ≤ t ≤ 2

To determine

To find: the length of the curve for the parametric equation x=t+e1 and y=te1 .

Explanation

Given:

The parametric equation for the variable x is as below.

x=t+e1

The parametric equation for the variable y is as below.

y=te1

Calculation:

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

L=αβ(dxdt)2+(dydt)2dt

Differentiate the variable x with respect to t .

dxdt=1+et

Differentiate the variable y with respect to t .

dydt=1e1

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+et) for dxdt and (1e1) for dydt in the above equation

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