Chapter 8.1, Problem 5E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### 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.5. y = x − ln x, 1 ≤ x ≤ 4

To determine

To represent: An integral as the length of the curve.

The length of the curve.

Explanation

Given information:

The curve function is y=xâˆ’lnx (1)

The limits are a=1 and b=4.

Calculation:

The expression to find the length of the curve is shown below:

L=âˆ«ab1+(dydx)2dx (2)

Here, the derivative of the function y is dydx, the lower limit is a, and the upper limit is b.

Differentiate Equation (1) with respect to x

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