Difficulty with washer method when revolving around axis other than y or x axis.

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SUMMARY

The discussion focuses on calculating the volume of a solid of revolution using the washer method for the region bounded by the curve y=-x^3, the x-axis, and the line x=-1, revolved around the line x=-2. The key formula involves integrating the difference between the squares of the outer and inner radii, multiplied by π. The challenge arises in expressing the radii correctly when the axis of rotation is not the x or y-axis, specifically converting the equations to accommodate the line x=-2.

PREREQUISITES
  • Understanding of the washer method for calculating volumes of revolution
  • Familiarity with curve equations and their transformations
  • Knowledge of integration techniques in calculus
  • Ability to interpret graphs of functions
NEXT STEPS
  • Study the washer method in detail, focusing on examples involving non-standard axes of rotation
  • Learn how to convert equations of curves from Cartesian to different axes
  • Practice integration of functions involving squared terms for volume calculations
  • Explore graphing tools to visualize functions and their revolutions
USEFUL FOR

Students studying calculus, particularly those focusing on volumes of solids of revolution, as well as educators seeking to clarify the washer method's application in complex scenarios.

bah
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Homework Statement


The region in the second quadrant bounded above by the curve y=-x^3, below by the x-axis, and on the left by the line x=-1, about the line x=-2


Homework Equations



It's basically the big radius squared minus the small radius squared, integrated in terms of y, and multiply that by pi, I think. But I have a hard time coming up the with expression for that when it's revolved around something other than the x or y axis... Please help?

The Attempt at a Solution



Well, the curve in terms of y is x=(-y)^(1/3). I have a hard time adjusting that so it is the right equation for the big radius, and adjusting the x=-1 so it is the small radius...
 
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Wow that is an interesting washer o.o.

Well if it's about the line x=-2 and you want to change it to the y -axis. What is the y-axis? x=? how can you change x=-2 to x=(y-axis)?

also look at a graph of this function. What are the limits? x=-1, and x=? You also need these for when you change x=(y-axis).
 
Last edited:
wow I'm really confused by this problem. it's been a while since I've done volumes but i figure i could at least get somewhere.

thinking thinking :)
 

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