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

In summary, the conversation discusses finding the volume of a solid formed by rotating a region in the second quadrant bounded by a curve, the x-axis, and two lines. The individual provides a general formula for finding the volume and struggles with adjusting the equation for a curved surface and changing the axis of rotation. They also consider the limits of integration and express confusion about the problem.
  • #1
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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  • #2
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:
  • #3
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 :)
 

1. What is the washer method when revolving around an axis other than the x or y axis?

The washer method is a mathematical technique used to find the volume of a solid of revolution. It involves slicing the solid into thin discs, calculating the volume of each disc, and then adding them together to find the total volume. When revolving around an axis other than the x or y axis, the radius of each disc is measured perpendicular to the axis of rotation.

2. How do I determine the radius of each disc when using the washer method for a non-x or y axis?

The radius of each disc is determined by finding the distance from the axis of rotation to the edge of the solid at each point. This distance is measured perpendicular to the axis of rotation. It may be helpful to draw a cross-section of the solid to better visualize the radius at each point.

3. Can the washer method be used for any shape when revolving around a non-x or y axis?

Yes, the washer method can be used for any shape when revolving around a non-x or y axis. As long as the shape can be sliced into thin discs, the method can be applied. This includes shapes with holes or irregular curves.

4. What is the formula for finding the volume of a solid using the washer method for a non-x or y axis?

The formula for finding the volume of a solid using the washer method for a non-x or y axis is V = ∫abπ(R(x)^2 - r(x)^2)dx, where a and b are the limits of integration, R(x) is the outer radius of the disc, and r(x) is the inner radius of the disc.

5. Are there any common mistakes to watch out for when using the washer method for a non-x or y axis?

One common mistake to watch out for is using the wrong axis of rotation. Make sure to carefully determine which axis you are revolving around and measure the radius perpendicular to that axis. Another mistake to avoid is not setting up the integral correctly. Pay attention to the limits of integration and the functions used for the outer and inner radii.

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