Explanation Given information: The polar curve is r = cos 2 θ 2 , 0 ≤ θ ≤ π . Formula used: The surface area of the polar curve r = f ( θ ) for a ≤ θ ≤ b is given by S = 2 π ∫ a b r sin θ r 2 + ( d r d θ ) 2 d θ Calculation: r = cos 2 θ 2 , 0 ≤ θ ≤ π (Given) Differentiating with respect to ‘ θ ’, we get d r d θ = − 2 cos θ 2 sin θ 2 1 2 = − cos θ 2 sin θ 2 The length of the polar curve r = cos 2 θ 2 for 0 ≤ θ ≤ π is given by S = 2 π ∫ 0 π r sin θ r 2 + ( d r d θ ) 2 d θ = 2 π ∫ 0 π ( cos 2 θ 2 ) sin θ ( cos 2 θ 2 ) 2 + ( − cos θ 2 sin θ 2 ) 2 d θ = 2 π ∫ 0 π ( cos 2 θ 2 ) sin θ ( cos 2 θ 2 ) ( cos 2 θ 2 + sin 2 θ 2 ) d θ = 2 π

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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Chapter 6.4, Problem 40PS

To determine

To find:The surface area generated by the polar curves r=cos2θ2,0≤θ≤π when revolving about the x-axis.

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Chapter 6.4, Problem 39PS

Chapter 6.4, Problem 41PS

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Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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The surface area generated by the polar curves r = cos 2 θ 2 , 0 ≤ θ ≤ π when revolving about the x-axis.

Solution Summary: The author calculates the surface area generated by the polar curves r=mathrmcos2theta 2.

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To find:The surface area generated by the polar curves r=cos2θ2,0≤θ≤π when revolving about the x-axis.

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Chapter 6 Solutions