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