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Chapter 6: Q. 56 (page 540)

You may have noticed that even very simple functions give rise to arc length integrals that we have no idea how to compute. In Exercises 53鈥�56, use a graphing calculator to approximate a definite integral that represents the arc length of the given function f(x) on the interval[a, b].

f(x)=lnx,[a,b]=[1,3]

Short Answer

Expert verified

By using a graphing calculator the approximate arc length of the given function on the given interval is2.30199.

Step by step solution

01

Step 1. Given Information.

The given function is f(x)=lnxand the interval is1,3.

02

Step 2. Find the arc length.

We have to use a graphing calculator to approximate a definite integral that represents the arc length of the given function f(x)=lnxon the interval 1,3.

So, the arc length of a function from the given interval is given by 鈭�ab1+(f'(x))2dx.

Thus, the arc length of the given function on the given interval is role="math" localid="1650700995895" 鈭�131+1x2dx=鈭�131+1x2dx

Now, by using the graphing calculator the approximate arc length of the definite integral is鈭�131+1x2dx鈮�2.30199.

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