Explanation Given: the region bounded by the lines x = 0 , x = 1 , y = x + 1 , and y = x + 2 Calculation: Consider the region bounded by the lines x = 0 , x = 1 , y = x + 1 and y = x + 2 . Use the Washer Method: "Suppose f and g are continuous functions on [a, b] with f ( x ) ≥ g ( x ) ≥ 0 . If R is the outer curve y = f ( x ) and r is the inner curve y = g ( x ) , and the region bounded by y = f ( x ) , y = g ( x ) , x = a and x = b is revolved about the x-axis, it generates a solid with volume V = ∫ a b π [ { f ( x ) } 2 − { g ( x ) } 2 ] d x ′ ′ The function y = x + 2 is greater than y = x + 1 as x + 2 ≥ x + 1 in the interval [ 0 , 1 ] , substitute f ( x ) = x + 2 ,

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6.2, Problem 16PS

To determine

To find: the volume of the solid

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Chapter 6.2, Problem 15PS

Chapter 6.2, Problem 17PS

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Chapter 6 Solutions

Calculus

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the volume of the solid

Solution Summary: The author calculates the volume of the solid by revolving the given region about the x-axis.

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Chapter 6 Solutions