Disk, Washer, Shell Multiple Integrals

[whatlifeforme]

Homework Statement

Determine how many integrals are required for disk, washer, and shell method.

Homework Equations

x=3y^2 - 2 and x=y^2 from (-2,0) to (1,1) about x-axis.

The Attempt at a Solution

Since there are no breaks or abnormalities in the graph it appears that 1 integral will solve for each to me. I have no other way of looking at this problem.

how do i know when the disk method requires more than one integral?

 

[SammyS]

Homework Statement

Determine how many integrals are required for disk, washer, and shell method.

Homework Equations

x=3y^2 - 2 and x=y^2 from (-2,0) to (1,1)

The Attempt at a Solution

Since there are no breaks or abnormalities in the graph it appears that 1 integral will solve for each to me. I have no other way of looking at this problem.

how do i know when the disk method requires more than one integral?

What axis is this to be revolved around ?

 

[whatlifeforme]

What axis is this to be revolved around ?

sorry. about the x-axis.

evidently it will take two for disk and washer, and one for shell, but I'm not sure why.

 

[Mark44]

sorry. about the x-axis.

evidently it will take two for disk and washer, and one for shell, but I'm not sure why.

Have you drawn a sketch of the region that will be rotated?
Have you drawn a different sketch of the solid that results from the rotation?

If you haven't drawn both sketches, it will be very difficult to work this problem.

If you use disks/washers of width Δx, your 2nd drawing should show that they change shape at (0, 0), because the upper and lower edges change. This means you will need two integrals.

If you use cylindrical shells of width Δy, the left and right edges don't change, so a single integral will suffice.