Integration Volume: Disc vs Shell - What's the Difference?

[pavadrin]

there are the two types of volume integration which i am aware of, disc-integration and shell integration. What is the difference between these? where would each one? Also i was looking at shell integration on carious sites on the net, and i am still a little confused how the generic formula works. Could someone ever so kindly explain this to me?

many thanks,
pavadrin

 

[Dale]

The difference between disk and shell integration is where the axis of rotation is. Let's assume that you are integrating a solid of rotation of some f(x)dx. If the axis of rotation is parallel to the x-axis then you use disk integration, but if the axis of rotation is perpendicular to the x-axis then you use shell integration.

 

[chaoseverlasting]

How would you find the general vector equation of a solid of revolution?

 

[HallsofIvy]

"Disks" works, of course, by using disks- normally, the radius of the disk is the value of the function and you calculate the area by $\pi f(x)$, multiply by the "thickness", dx, and then integrate.

"Shells" works by using thin cylinders. The radius is typically the x-value so you have a "circumference" calculation $2\pi x$ and then multiply by the "height" of the cylinder, f(x): you integrate $2\pi x f(x) dx[/itex\.$

 

[pavadrin]

okay thanks for the replies
it is a little less confusing now
ill try reading into in more and repost if i am still stuck,
thanks once again for your time,
pavadrin