   Chapter 10.5, Problem 59E

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 = 1 θ ,       [ π , 2 π ] .

To determine

To graph: The polar equation r=1θ over the interval [π,2π] by the means of graphing utility and to determine the approximate length of the curve by by means of integration capability of graphing utility.

Explanation

Given:

The provided polar equation r=1θ over the interval [π,2π].

Formula used:

The arc length of polar curve is given by s=αβr2+(drdθ)2dθ.

Graph:

For the curve of polar equation use the following steps in TI_83 calculator:

Step 1: Open TI-83 calculator.

Step 2: Press MODE and select the Pol option.

Step 3: Press Y=.

Step 4: Enter r1=1θ.

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.

The curve is obtained as:

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