Volume of Revolution: y=5, y=x+4/x; x=-1

Click For Summary
SUMMARY

The discussion focuses on calculating the volume of revolution for the region bounded by the curves y=5 and y=x+4/x, rotated about the line x=-1. The shell method is identified as the most suitable approach for this problem. The correct volume of the solid generated is determined to be 8π(3-ln4). A common error noted in the calculations was the misplacement of parentheses, which led to an incorrect expression during the setup of the integral.

PREREQUISITES
  • Understanding of volume of revolution concepts
  • Familiarity with the shell method for integration
  • Basic knowledge of plotting curves and identifying bounded regions
  • Proficiency in manipulating algebraic expressions and parentheses
NEXT STEPS
  • Study the shell method for calculating volumes of revolution
  • Practice plotting curves and identifying bounded regions for integration
  • Learn about common pitfalls in algebraic manipulation, particularly with parentheses
  • Explore advanced integration techniques for volume calculations
USEFUL FOR

Students studying calculus, particularly those focusing on volume of revolution problems, as well as educators looking for examples of common errors in integration techniques.

mace2
Messages
101
Reaction score
0

Homework Statement


"The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method."

y=5, y=x+4/x; about x=-1


Homework Equations


Upon plotting it I decided it would be best to use the shell method. I'm not sure how to express it in your fancy symbols but I included all of my work as an attachment.


The Attempt at a Solution


Please see attachment. The correct answer is actually 8pi(3-ln4). I have gone over it a few times and I don't see what I did wrong. Any advice whatsoever would be great, thanks.

P.S. Sorry the image is grainy, I didn't know how to make it small enough to fit the guidelines and still be legible.
 

Attachments

  • Math 001.GIF
    Math 001.GIF
    230.7 KB · Views: 571
Physics news on Phys.org
Ah I just figured it out. I accidentally wrote 5-x+4/x, when i really meant 5-(x+4/x).

Stupid parantheses!
 
Perhaps it's not the parentheses that are stupid!:rolleyes:
 

Similar threads

Volume of revolution, region bounded by two functions
  • · Replies 1 ·
Replies
1
Views
2K
Volume of Revolution: Find V with Shell Method
  • · Replies 13 ·
Replies
13
Views
2K
Volume of revolution around the y-axis
  • · Replies 20 ·
Replies
20
Views
3K
Find the constrained maxima and minima of ##f(x,y,z)=x+y^2+2z##
  • · Replies 2 ·
Replies
2
Views
2K
Volume integral of x^2 + (y-2)^2 +z^2 = 4 where x , y , z > 0
  • · Replies 21 ·
Replies
21
Views
3K
Volume of revolution in the first quadrant?
  • · Replies 3 ·
Replies
3
Views
3K
Find the local maxima and minima for##f(x,y) = x^3-xy-x+xy^3-y^4##
  • · Replies 5 ·
Replies
5
Views
1K
The volume of a "spherical cap" using triple integrals
  • · Replies 9 ·
Replies
9
Views
2K
Volumes of Revolution Question
  • · Replies 3 ·
Replies
3
Views
1K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K