   Chapter 8.1, Problem 5E

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.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=xlnx (1)

The limits are a=1 and b=4.

Calculation:

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

L=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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