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

4th Edition

ISBN: 9781319308858

Author: Rogawski

Publisher: MAC HIGHER

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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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y2=x, y=x. What is the volume of the curve is rotated about the y-axis

2. Sketch the graphs of v = x2 – 6x + 12, x = 5, x-axis and y-axis. Shade the region bounded by the curves. Find the volume of the solid that is formed by revolving the region shaded about the y-axis.

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Chapter 6 Solutions

CALCULUS:EARLY TRANS.(LL)-W/ACCESS

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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Prob. 29CRE Ch. 6 - Prob. 30CRE Ch. 6 - Prob. 31CRE Ch. 6 - Prob. 32CRE Ch. 6 - Prob. 33CRE Ch. 6 - Prob. 34CRE Ch. 6 - Prob. 35CRE Ch. 6 - Prob. 36CRE Ch. 6 - Prob. 37CRE Ch. 6 - Prob. 38CRE Ch. 6 - Prob. 39CRE Ch. 6 - Prob. 40CRE Ch. 6 - Prob. 41CRE Ch. 6 - Prob. 42CRE Ch. 6 - Prob. 43CRE Ch. 6 - Prob. 44CRE Ch. 6 - Prob. 45CRE Ch. 6 - Prob. 46CRE Ch. 6 - Prob. 47CRE Ch. 6 - Prob. 48CRE Ch. 6 - Prob. 49CRE Ch. 6 - Prob. 50CRE Ch. 6 - Prob. 51CRE Ch. 6 - Prob. 52CRE Ch. 6 - Prob. 53CRE Ch. 6 - Prob. 54CRE

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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!

Concept explainers

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

Want to see the full answer?

Chapter 6 Solutions

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

x23+y23=1