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 ,

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 6.2, Problem 16PS

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To find: the volume of the solid

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Chapter 6.2, Problem 15PS

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8) The volume of the region in the second quadrant bounded above by y=-x3, below by the x-axis and on the left by the line x=-1, revolved about the line x=-2 is: (3/5)pi C. units. ○ (2/5)pi C. units. ○ (5/3)pi C. units ○ (5/2)pi C. units.

1. Suppose a new theater being designed has a base which can be described as the region bounded by y = 4x² and y = 25. The cross-sections perpendicular to the y-axis will be rectangles whose height is 5 units higher than the width of its base. (a) Find an exact value A so that the line y = A divides the floor into two equal areas. (b) Find the (approximate) percentage of the volume of the theater which is in the region y2 A. Give your answer to two decimal places.

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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