Explanation Given information: The polar curve is r = csc θ , π 4 ≤ θ ≤ π 3 . 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 = csc θ , π 4 ≤ θ ≤ π 3 (Given) Differentiating with respect to ‘ θ ’, we get d r d θ = − csc θ cot θ The length of the polar curve r = csc θ for π 4 ≤ θ ≤ π 3 is given by S = 2 π ∫ π 4 π 3 r sin θ r 2 + ( d r d θ ) 2 d θ = 2 π ∫ π 4 π 3 ( csc θ ) sin θ ( csc θ ) 2 + ( − csc θ cot θ ) 2 d θ = 2 π ∫ π 4 π 3 ( csc θ

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 6.4, Problem 39PS

To determine

To find:The surface area generated by the polar curves r=cscθ,π4≤θ≤π3 when revolving about the x-axis.

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Chapter 6.4, Problem 38PS

Chapter 6.4, Problem 40PS

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Chapter 6 Solutions

Calculus

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The surface area generated by the polar curves r = csc θ , π 4 ≤ θ ≤ π 3 when revolving about the x-axis.

Solution Summary: The author calculates the surface area generated by the polar curves r=mathrmcsctheta,pi 4le

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To find:The surface area generated by the polar curves r=cscθ,π4≤θ≤π3 when revolving about the x-axis.

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Chapter 6 Solutions