Explanation Given information: The given equationhas a revolution about the x-axis: x 2 3 + y 2 3 = 1 Concept used: If f is continuous and f ( x ) ≥ 0 on [ a , b ] , then the solid obtained by rotating the region under the graph about the x-axis has the volume: V = π ∫ a b R 2 d x = π ∫ a b f ( x ) 2 d x Integration of ∫ a b a n d x = 1 n + 1 a n + 1 ( a − b ) 3 = a 3 − 3 a 2 b + 3 a b 2 − b 3 Calculation: The given equation: x 2 3 + y 2 3 = 1 y 2 3 = 1 − x 2 3 y = ± ( 1 − x 2 3 ) 3 2 So, the limit for equation y are − 1 and 1 . Here , a = − 1 , b = 1 Put the value of f ( x ) in given formula and solve the function: V = π ∫ a b f ( x ) 2 d x V = π ∫ − 1 1 [ ( 1 − x 2 3 ) 3 2 ] 2 d x V = π ∫ − 1 1 ( 1 − x 2 3 ) 3 d x V = π ∫ − 1 1 [ ( 1 ) 3 − 3 × ( 1 ) 2 × x 2 3 + 3 × 1 × ( x 2 3 ) 2 − ( x 2 3 ) 3 ] d x

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 6.3, Problem 61E

To determine

Calculate the volume of revolution about x-axis for the equation and draw the hypocycloid:

x23+y23=1

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Chapter 6.3, Problem 60E

Chapter 6.3, Problem 62E

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Chapter 6 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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Calculate the volume of revolution about x-axis for the equation and draw the hypocycloid: x 2 3 + y 2 3 = 1

Solution Summary: The author calculates the volume of revolution about x-axis for the equation and draws the hypocycloid: xraisebox1ex2!

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Calculate the volume of revolution about x-axis for the equation and draw the hypocycloid:

x23+y23=1

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Chapter 6 Solutions

Calculate the volume of revolution about x-axis for the equation and draw the hypocycloid: x 2 3 + y 2 3 = 1

Solution Summary: The author calculates the volume of revolution about x-axis for the equation and draws the hypocycloid: xraisebox1ex2!

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Calculate the volume of revolution about x-axis for the equation and draw the hypocycloid: x23+y23=1

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Chapter 6 Solutions

Calculate the volume of revolution about x-axis for the equation and draw the hypocycloid:

x23+y23=1