   Chapter 10.5, Problem 57E

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 = 2 θ ,       [ 0 , π 2 ]

To determine

To graph: The polar equation r=2θ over the interval [0,π2] by the use of graphing utility and to determine the approximate length of the curve by using integration capability of graphing utility.

Explanation

Given:

Polar equation r=2θ over the interval [0,π2].

Formula used:

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

Graph:

For the curve of polar equation use TI-83 as graphing utility and follow these steps:

Step 1: Open TI-83 calculator.

Step 2: Press MODE and select the Pol option.

Step 3: Press Y=.

Step 4: Enter r1=2θ.

Step 5: Press WINDOW to access window editor.

Step 6: Set window as

θmin=0,θmax=π2,θstep=0.1308996,Xmin=1,Xmax=5,Xscl=1,Ymin=1,Ymax=5,Yscl=1.

Step 7: Press TRACE.

The curve obtained is

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