Help with washers method about a line

In summary: Then solve for x and y. In summary, the student is trying to solve for a line but has no idea how to do it.
  • #1
Toanizzle
2
0
help with washers method about a line :(

Homework Statement


We are given two curves y=sin(x) and y=0. Use washers to revolve this around the line y=-2 from 0 to pi.

Homework Equations


The Attempt at a Solution


I kno that the equation is 2pi Int( height x radius x thickness), but i have absolutely no idea what to plug in and how to figure out where these things come from :(
I kno how to do it about the x axis, by using pi Int(R(x)-r(x))dx but how do i do it about the line y=-2?
 
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  • #2


im sorry if i haven't had enough of an attempt but I am completely lost right no :(
 
  • #3


Toanizzle said:

Homework Statement


We are given two curves y=sin(x) and y=0. Use washers to revolve this around the line y=-2 from 0 to pi.


Homework Equations





The Attempt at a Solution


I kno that the equation is 2pi Int( height x radius x thickness), but i have absolutely no idea what to plug in and how to figure out where these things come from :(
I kno how to do it about the x axis, by using pi Int(R(x)-r(x))dx but how do i do it about the line y=-2?
It would be a good idea to start by stating the problem correctly! "Use washers to revolve this around the line y= 2 from 0 to pi" makes no sense. You don't need "washers" or "disks" or "shells" to revolve anything. You need those to find the volume or the surface area. Was the problem "find the volume of the solid created by revolving around the line y=-2" or "find the surface area of the solid created by revolving around the line y=-2"?

One reason I say that is because "use washers" imply you are finding the volume but the formula you say you "know" is for surface area. We can't help you until you tell us what the problem really is.
 
  • #4


Toanizzle said:

Homework Statement


We are given two curves y=sin(x) and y=0. Use washers to revolve this around the line y=-2 from 0 to pi.


Homework Equations





The Attempt at a Solution


I kno that the equation is 2pi Int( height x radius x thickness), but i have absolutely no idea what to plug in and how to figure out where these things come from :(
I kno how to do it about the x axis, by using pi Int(R(x)-r(x))dx but how do i do it about the line y=-2?

Have you sketched a graph of the region to be revolved? After you do that, draw a sketch of the cross section in the x-y plane of the solid of revolution. A typical volume element will look like a washer (a disk with a hole in it). Find an expression that gives the volume of your typical volume element, and that will be essentially your integrand.
 

What is the "washers method" in relation to a line?

The washers method is a mathematical technique used to find the volume of a solid shape created by rotating a two-dimensional region around a line.

How do you use the washers method to find the volume of a solid?

To use the washers method, you must first identify the two-dimensional region being rotated around a line. Then, you must set up an integral that represents the volume of a single washer (a cylindrical slice of the solid). Finally, you must integrate the function and solve for the total volume.

What is the difference between the "washers method" and the "shells method"?

The washers method is used when the shape being rotated has a hole in the middle, whereas the shells method is used when the shape being rotated does not have a hole. Additionally, the washers method uses cylindrical slices to find volume, while the shells method uses cylindrical shells.

What are the limitations of using the washers method?

The washers method can only be used to find the volume of solids that can be formed by rotating a two-dimensional region around a line. It cannot be used for more complex shapes or for finding other properties of the solid, such as surface area or center of mass.

Can the washers method be used for non-uniform solids?

Yes, the washers method can be used for non-uniform solids as long as the function being integrated is representative of the cross-sectional area of the solid at each point along the line of rotation.

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