Short Answer

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
One petal of the polar rose $r = \cos 4 θ$

The integral can be given as $2 \int_{0}^{\frac{π}{8}} \sqrt{\cos^{2} 4 θ + 16 \sin^{2} 4 θ} d θ$ and the arc length can be given as 2.14units.

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Step by Step Solution

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TABLE OF CONTENTS

Step 1: Given information

We are given the equation as $r = \cos 4 θ$

Step 2: Evaluate

We know that the arc length of one petal of the polar rose $r = \cos (n θ)$ can be given as

$2 \int_{0}^{\frac{π}{2 n}} \sqrt{\cos^{2} n θ + n^{2} \sin^{2} θ} d θ P u t n = 4 w e g e t, 2 \int_{0}^{\frac{π}{8}} \sqrt{\cos^{2} 4 θ + 16 \sin^{2} 4 θ} d θ$

Using a CAS calculator we get,

$L = 2 (1.07) L = 2.14 u n i t$

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Calculus

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Short Answer

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
One petal of the polar rose $r = \cos 4 θ$

Step by Step Solution

Step 1: Given information

Step 2: Evaluate

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Calculus

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Short Answer

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral One petal of the polar rose r=cos4θ

Step by Step Solution

Step 1: Given information

Step 2: Evaluate

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in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
One petal of the polar rose $r = \cos 4 θ$