   Chapter 10.5, Problem 60E

Chapter
Section
Textbook Problem

# Finding the Arc Length of a Polar Curve In Exercises 59-64, use a graphing utility to graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve. r = e θ ,       [ 0 , π ]

To determine

To graph: The polar equation r=eθ over the interval [0,π] by the use of graphing utility. Also, to determine the approximate length of the curve by the use of integration capability of graphing utility.

Explanation

Given:

The polar equation r=eθ over the interval [0,π].

Formula used:

Arc length of polar curve is s=αβr2+(drdθ)2dθ.

Graph:

Use the following steps in TI-83 for the curve of polar equation:

Step 1:

Open TI-83 calculator.

Step 2:

Press MODE and select the Pol option.

Step 3:

Press Y=.

Step 4:

Enter r1=eθ.

Step 5:

Press WINDOW to access window editor.

Step 6:

Set window as

θmin=π,θmax=2π,θstep=0.1308996,Xmin=0.5,Xmax=0.5,Xscl=1,Ymin=0.5,Ymax=0.5,Yscl=1

Step 7:

Press TRACE

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