Determining best method for volumes?

[dnt]

Homework Statement

No specific question but what is the best way to determine which method is the best for solving for volumes (using integration) of shapes as they revolve around axis/lines. disk method? washer method? shell method? other?

what exactly do you look for that may hint towards one method over the other?

Homework Equations

n/a

The Attempt at a Solution

 

[Nibbler]

It depends on what axis they're revolving.

 

[HallsofIvy]

Which is better depends not only about which axis they are revolving but also the specific form of the functions describing the boundaries. About the only thing one can say in general is to consider each and decide which gives the simplest integral.

 

[dnt]

well you only have two axis, right? if its x which is best? if its y which is best?

 

[mjsd]

to do volume with calculus: whether you chop the object up into thin disks or thin shells depends highly on the shape of the object. eg: consider the area under the graph e^(-x) and x in [1,2], if vol. is formed by revolving this area about x axis, then disk method is the natural choice, whereas if revolved about y axis, then shell method would be better.

 

[dnt]

why? what made you pick one over the other? what specifics do you look for that would cause you to lean towards one method over the other?

 

[Nibbler]

Because one of the methods is easier than the other. In certain situations, the shell method is easier to do than the disk method.

And we all know mathematicians are lazy. ;)

Think about it this way: if you were to find the area of a cone (y = x) that revolved around the x-axis, you'ld use the disk method. Not saying that you can't use the shell method, but its just easier to use disk.