Explanation Given information: The polar curve is f ( θ ) = cos θ for 0 ≤ θ ≤ π 6 . Formula used: The area of the polar region enclosed by f ( θ ) = cos θ for a ≤ θ ≤ b is given by A = 1 2 ∫ a b [ f ( θ ) ] 2 d θ . Calculation: f ( θ ) = cos θ for 0 ≤ θ ≤ π 6 (Given) The area of the polar region enclosed by f ( θ ) = cos θ for 0 ≤ θ ≤ π 6 is given by A = 1 2 ∫ 0 π 6 [ f ( θ ) ] 2 d θ = 1 2 ∫ 0 π 6 cos 2 θ d θ = 1 2 ∫ 0 π 6 1

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 31PS

To determine

To find:The area of the polar region enclosed by f(θ)=cosθ for 0≤θ≤π6 .

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Chapter 6.3, Problem 30PS

Chapter 6.3, Problem 32PS

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Chapter 6 Solutions

Calculus

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The area of the polar region enclosed by f ( θ ) = cos θ for 0 ≤ θ ≤ π 6 .

Solution Summary: The author calculates the area of the polar region enclosed by f(theta )=mathrmcos

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To find:The area of the polar region enclosed by f(θ)=cosθ for 0≤θ≤π6 .

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Chapter 6 Solutions