Axis of revolution-washer/disks

[emk]

Y=x^2, y=0, x=1 ; about x=2

v=pi r^2 T

I tried 0 to 1 intg (x^3-2)^2+2^2 dx, but it wasn't right. Not sure what to do.

 

[SteamKing]

We're not sure what you are doing, either.

Use the homework template and give a complete problem statement.

 

[QuarkCharmer]

It may help to break that thing up into two different integrals. The thing is shaped like a circus tent. That is, a cylinder with a spire on top. The cylinder integration can be done without calculus. Then do the spire part using your books formula (the formula for volume basically) and add the two.

 

[verty]

It may help to break that thing up into two different integrals. The thing is shaped like a circus tent. That is, a cylinder with a spire on top. The cylinder integration can be done without calculus. Then do the spire part using your books formula (the formula for volume basically) and add the two.

I see no spire on top, just an oddly-shaped cylinder.

 

[haruspex]

I see no spire on top, just an oddly-shaped cylinder.

QuarkCharmer's description makes sense to me. The point of the spire is at x=2, the axis of revolution. But the washer method just seems to complicate matters. emk, were you told to use that method here?

 

[emk]

QuarkCharmer's description makes sense to me. The point of the spire is at x=2, the axis of revolution. But the washer method just seems to complicate matters. emk, were you told to use that method here?

Yes, either the disk or washer method.

 

[QuarkCharmer]

Unless I am mistaken:

You could easily find all these intersection points, and rewrite the equation to integrate such that the integration makes more sense to you.

Hope that is helpful.