Explanation Given: The given equation is y = 12 − 4 x a n d y = 8 x − 12 . The graph is shown below: Formula Used: If x = f ( y ) a n d x = g ( y ) rotated about the y-axis over the given interval a ≤ y ≤ b then the volume of solid revolution is calculated by V = π ∫ a b ( ( f ( y ) ) 2 − ( g ( y ) ) 2 ) Calculation: First, solve the equation y = 12 − 4 x for x, we get x = 1 4 ( 12 − y ) Now, solve the equation y = 8 x − 12 for x, we get x = 1 8 ( y + 12 ) So, the first interval 4 ≤ y ≤ 12 , the cross section of the disk with radius 1 4 ( 12 − y ) and second interval − 12 ≤ y ≤ 4 , the cross section of the disk with radius 1 8 ( y + 12 ) Therefore, the volume of the solid revolution is V = π ∫ − 12 4 ( 1 8 ( y + 12 ) ) 2 + π ∫ 4 12 ( 1 4 ( 12 − y ) ) 2 = π 64 ∫ − 12 4 ( y + 12 ) 2 d y + π 16 ∫ 4 12 ( 12 − y ) 2 d y

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 6.3, Problem 25E

To determine

the volume as a sum of two integrals, one for $- 12 \leq y \leq 4$ and $4 \leq y \leq 12$ .

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Chapter 6.3, Problem 24E

Chapter 6.3, Problem 26E

Chapter 6 Solutions

CALCULUS (CLOTH)

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

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the volume as a sum of two integrals, one for − 12 ≤ y ≤ 4 and 4 ≤ y ≤ 12 .

Solution Summary: The author calculates the volume of the solid revolution as a sum of two integrals.

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the volume as a sum of two integrals, one for $- 12 \leq y \leq 4$ and $4 \leq y \leq 12$ .

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Chapter 6 Solutions

the volume as a sum of two integrals, one for − 12 ≤ y ≤ 4 and 4 ≤ y ≤ 12 .

Solution Summary: The author calculates the volume of the solid revolution as a sum of two integrals.

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the volume as a sum of two integrals, one for −12≤y≤4 and 4≤y≤12.

Want to see the full answer?

Chapter 6 Solutions

the volume as a sum of two integrals, one for $- 12 \leq y \leq 4$ and $4 \leq y \leq 12$ .