Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Question
Chapter A5.1, Problem 43E
To determine
To find: the volume of the solid.
Expert Solution & Answer
Answer to Problem 43E
The volume of the solid is V=24π .
Explanation of Solution
Given:
The line x=4, and the hyperbola x2−y2=1 .
Calculation:
Equation of hyperbola: x2−y2=1 .
This implies that,
x2=y2+1
x=±√y2+1
Since y cannot be negative, use the positive root on the interval −3≤y≤3 .
V=∫3−3π(√y2+1)2⋅dy
=2∫30π(y2+1)⋅dy
=2π[13y3+y]30
=24π
Therefore, V=24π .
Conclusion:
Therefore, the volume of the solid is V=24π .
Chapter A5 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Ch. A5.1 - Prob. 1ECh. A5.1 - Prob. 2ECh. A5.1 - Prob. 3ECh. A5.1 - Prob. 4ECh. A5.1 - Prob. 5ECh. A5.1 - Prob. 6ECh. A5.1 - Prob. 7ECh. A5.1 - Prob. 8ECh. A5.1 - Prob. 9ECh. A5.1 - Prob. 10E
Ch. A5.1 - Prob. 11ECh. A5.1 - Prob. 12ECh. A5.1 - Prob. 13ECh. A5.1 - Prob. 14ECh. A5.1 - Prob. 15ECh. A5.1 - Prob. 16ECh. A5.1 - Prob. 17ECh. A5.1 - Prob. 18ECh. A5.1 - Prob. 19ECh. A5.1 - Prob. 20ECh. A5.1 - Prob. 21ECh. A5.1 - Prob. 22ECh. A5.1 - Prob. 23ECh. A5.1 - Prob. 24ECh. A5.1 - Prob. 25ECh. A5.1 - Prob. 26ECh. A5.1 - Prob. 27ECh. A5.1 - Prob. 28ECh. A5.1 - Prob. 29ECh. A5.1 - Prob. 30ECh. A5.1 - Prob. 31ECh. A5.1 - Prob. 32ECh. A5.1 - Prob. 33ECh. A5.1 - Prob. 34ECh. A5.1 - Prob. 35ECh. A5.1 - Prob. 36ECh. A5.1 - Prob. 37ECh. A5.1 - Prob. 38ECh. A5.1 - Prob. 39ECh. A5.1 - Prob. 40ECh. A5.1 - Prob. 41ECh. A5.1 - Prob. 42ECh. A5.1 - Prob. 43ECh. A5.1 - Prob. 44ECh. A5.1 - Prob. 45ECh. A5.1 - Prob. 46ECh. A5.2 - Prob. 1ECh. A5.2 - Prob. 2ECh. A5.2 - Prob. 3ECh. A5.2 - Prob. 4ECh. A5.2 - Prob. 5ECh. A5.2 - Prob. 6ECh. A5.2 - Prob. 7ECh. A5.2 - Prob. 8ECh. A5.2 - Prob. 9ECh. A5.2 - Prob. 10ECh. A5.2 - Prob. 11ECh. A5.2 - Prob. 12ECh. A5.2 - Prob. 13ECh. A5.2 - Prob. 14ECh. A5.2 - Prob. 15ECh. A5.2 - Prob. 16ECh. A5.2 - Prob. 17ECh. A5.2 - Prob. 18ECh. A5.2 - Prob. 19ECh. A5.2 - Prob. 20ECh. A5.2 - Prob. 21ECh. A5.2 - Prob. 22ECh. A5.2 - Prob. 23ECh. A5.2 - Prob. 24ECh. A5.2 - Prob. 25ECh. A5.2 - Prob. 26ECh. A5.2 - Prob. 27ECh. A5.2 - Prob. 28ECh. A5.3 - Prob. 1ECh. A5.3 - Prob. 2ECh. A5.3 - Prob. 3ECh. A5.3 - Prob. 4ECh. A5.3 - Prob. 5ECh. A5.3 - Prob. 6ECh. A5.3 - Prob. 7ECh. A5.3 - Prob. 8ECh. A5.3 - Prob. 9ECh. A5.3 - Prob. 10ECh. A5.3 - Prob. 11ECh. A5.3 - Prob. 12ECh. A5.3 - Prob. 13ECh. A5.3 - Prob. 14ECh. A5.3 - Prob. 15ECh. A5.3 - Prob. 16ECh. A5.3 - Prob. 17ECh. A5.3 - Prob. 18ECh. A5.3 - Prob. 19ECh. A5.3 - Prob. 20ECh. A5.3 - Prob. 21ECh. A5.3 - Prob. 22ECh. A5.3 - Prob. 23ECh. A5.3 - Prob. 24ECh. A5.3 - Prob. 25ECh. A5.3 - Prob. 26ECh. A5.3 - Prob. 27ECh. A5.3 - Prob. 28ECh. A5.3 - Prob. 29ECh. A5.3 - Prob. 30ECh. A5.3 - Prob. 31ECh. A5.3 - Prob. 32ECh. A5.3 - Prob. 33ECh. A5.3 - Prob. 34ECh. A5.3 - Prob. 35ECh. A5.3 - Prob. 36ECh. A5.3 - Prob. 37ECh. A5.3 - Prob. 38ECh. A5.3 - Prob. 39ECh. A5.3 - Prob. 40ECh. A5.3 - Prob. 41ECh. A5.3 - Prob. 42ECh. A5.3 - Prob. 43ECh. A5.3 - Prob. 44ECh. A5.3 - Prob. 45ECh. A5.3 - Prob. 46E
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