Explanation Given information: The region is the right of the line r cos θ = 1 and inside the lemniscate r 2 = 2 sin 2 θ . 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 = 2 sin 2 θ and the line r cos θ = 1 (Given) To find the point of intersection of the line r cos θ = 1 and lemniscate r 2 = 2 sin 2 θ ,. r 2 = 2 sin 2 θ ⇒ 1 cos 2 θ = 2 sin 2 θ ⇒ 1 2 = cos 2 θ sin 2 θ ⇒ θ = π 4 , 3.4287

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 6.3, Problem 51PS

To determine

To find:The area to the right of the line rcosθ=1 and inside the lemniscate r2=2sin2θ .

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Chapter 6.3, Problem 50PS

Chapter 6.3, Problem 52PS

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Chapter 6 Solutions

Calculus

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The area to the right of the line r cos θ = 1 and inside the lemniscate r 2 = 2 sin 2 θ .

Solution Summary: The area to the right of the line rmathrmcostheta =1 and inside the lemniscate

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To find:The area to the right of the line rcosθ=1 and inside the lemniscate r2=2sin2θ .

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Chapter 6 Solutions