Explanation Given information: The region is the of the lemniscate r 2 = 8 cos 2 θ that lies in the region r ≥ 2 . Formula used: The area of the polar region enclosed by f ( θ ) for a ≤ θ ≤ b is given by A = 1 2 ∫ a b [ f ( θ ) ] 2 d θ . Calculation: r 2 = 8 cos 2 θ and r = 2 .(Given) To find the point of intersection of r 2 = 8 cos 2 θ and r = 2 , 8 cos 2 θ = 4 . 2 cos 2 θ = 1 cos 2 θ = 1 2 2 θ = cos − 1 1 2 θ = π 6

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6.3, Problem 48PS

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To find:The area of the portion of the lemniscate r2=8cos2θ that lies in the region r≥2 .

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Chapter 6.3, Problem 47PS

Chapter 6.3, Problem 49PS

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Chapter 6 Solutions

Calculus

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The area of the portion of the lemniscate r 2 = 8 cos 2 θ that lies in the region r ≥ 2 .

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To find:The area of the portion of the lemniscate r2=8cos2θ that lies in the region r≥2 .

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Chapter 6 Solutions