Explanation Given: The region bounded by the parabolic arc y = x , the y -axis, and the line y = 1 Calculation: Consider the region bounded by the parabolic arc y = x , the y -axis, and the line y = 1 Use the Shells Method, V = ∫ a b 2 π x f ( x ) d x The graph of the given region is as follows: Consider a strip parallel to y- axis in the given region. From the graph, the height of the strip will be, L = 1 − x Intersection point of two graphs will be computed as follows: x = 1 x = 1 2 = 1 So, intersection point of two graphs is ( 1 , 1 ) Thus, substitute f ( x ) = 1 − x , a = 0 And b = 1 , The volume of the solid formed by revolving the given region about the y- axis will be, V = ∫ 0 1 2 π

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ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6.2, Problem 20PS

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To find: the volume of the solid formed.

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Chapter 6.2, Problem 19PS

Chapter 6.2, Problem 21PS

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Chapter 6 Solutions

Calculus

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the volume of the solid formed.

Solution Summary: The author calculates the volume of the solid formed by revolving the given region about the y-axis using the Shells Method.

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Chapter 6 Solutions