Explanation Given information: The polar curve is r = θ 2 , 0 ≤ θ ≤ 1 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 = θ 2 , 0 ≤ θ ≤ 1 (Given) Differentiating with respect to ‘ θ ’, we get d r d θ = 2 θ Given that 0 ≤ θ ≤ 1 The length of the polar curve r = θ 2 for 0 ≤ θ ≤ 1 is given by S = ∫ 0 1 r 2 + ( d r d θ ) 2 d θ = ∫ 0 1 ( θ 2 ) 2 + ( 2 θ ) 2

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 33PS

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To find:The length of the polar curves r=θ2 , 0≤θ≤1

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Chapter 6.4, Problem 32PS

Chapter 6.4, Problem 34PS

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Chapter 6 Solutions

Calculus

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The length of the polar curves r = θ 2 , 0 ≤ θ ≤ 1

Solution Summary: The length of the given polar curve is 1.06 units.

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Chapter 6 Solutions