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

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6.4, Problem 38PS

To determine

To find:The surface area generated by the polar curves r=1−cosθ,0≤θ≤π when revolving about the x-axis.

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Chapter 6.4, Problem 37PS

Chapter 6.4, Problem 39PS

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Chapter 6 Solutions

Calculus

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The surface area generated by the polar curves r = 1 − cos θ , 0 ≤ θ ≤ π when revolving about the x-axis.

Solution Summary: The author calculates the surface area generated by the given polar curve, 325pi square units.

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To find:The surface area generated by the polar curves r=1−cosθ,0≤θ≤π when revolving about the x-axis.

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Chapter 6 Solutions