Explanation Given information: The polar curve is r = cos θ . Formula used: The length of the polar curve r = f ( θ ) for a ≤ θ ≤ b is given by S = ∫ a b r 2 + ( d r d θ ) 2 d θ Calculation: r = cos θ (Given) Differentiating with respect to ‘ θ ’, we get d r d θ = − sin θ We know that 0 ≤ θ ≤ π The length of the polar curve r = cos θ for 0 ≤ θ ≤ π is given by S = ∫ 0 π <

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.4, Problem 29PS

To determine

To find:The length of the polar curves r=cosθ

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Chapter 6.4, Problem 28PS

Chapter 6.4, Problem 30PS

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3. You want to manufacture a fruity cake in a unique shape. You designing a shape for a fruity cake by generating r=8 sin 0 – 2 sin 40 about the polar axis and make it 8 cm in height. You decide to pack it in a box. You need to know how much mixture of fruity cake to have on hand for a production run of ten boxes. Sketch the graph of r.

Chapter 6 Solutions

Calculus

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The length of the polar curves r = cos θ

Solution Summary: The author calculates the length of the given polar curve using r=mathrmcostheta .

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To find:The length of the polar curves r=cosθ

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Chapter 6 Solutions