   Chapter 10.2, Problem 42E

Chapter
Section
Textbook Problem

# Find the exact length of the curve.42. x = et − t, y = 4et/2, 0 ≤ t ≤ 2

To determine

To find: the exact length of the curve for the parametric equation x=ett and y=4et/2 .

Explanation

Given:

The parametric equation for the variable x is as below.

x=ett

The parametric equation for the variable y is as below.

y=4et/2

Calculation:

The length of the curve is obtained by the formula.

L=αβ(dxdt)2+(dydt)2dt

Differentiate the variable x with respect to t .

x=ettdxdt=et1

Differentiate the variable y with respect to t :

y=4et/2dydt=2et/2

Write the length of the curve formula.

L=αβ(dxdt)2+(dydt)2dt

Substitute (et1) for dxdt and (2et/2) for dydt in the above equation

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