Explanation Given data: x = t ( 1 − t ) (1) y = 1 + t 2 (2) Calculation: Since the graph bound about the y -axis, substitute 0 for x in equation (1) as follows. t ( 1 − t ) = 0 1 − t = 0 t = 1 Substitute 1 for t in equation (2) as follows. y = 1 + 1 2 = 1 + 1 = 2 Consider the expression to obtain the volume swept out by revolving region bounded by y -axis with a graph of x = t ( 1 − t ) , y = 1 + t 2 . Volume = ∫ 1 2 π x 2 d y Substitute t ( 1 − t ) for x as follows. Volume = ∫ 0 1 π [ t ( 1 − t ) ] 2 2 d t { ∵ d y = 2 d t }

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 10.2, Problem 50E

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Calculate the volume swept out by revolving region bounded by y-axis with a graph of x=t(1−t), y=1+t2.

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Chapter 10.2, Problem 49E

Chapter 10.2, Problem 51E

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Chapter 10 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...

Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 12E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 14E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - In Exercises 25–28, use the given graphs of x =...Ch. 10.1 - Finding Parametric Equations Find parametric...Ch. 10.1 - Find parametric equations and a parameter interval...Ch. 10.1 - Prob. 31E Ch. 10.1 - In Exercises 31–36, find a parametrization for the...Ch. 10.1 - 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Calculate the volume swept out by revolving region bounded by y-axis with a graph of x=t(1−t), y=1+t2.

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Chapter 10 Solutions