What method to use to calculate volume

[thushanthan]

Hi

Can anyone explain to me the difference between the following:

Single variable Calculus : Solids of Revolution

Multivariable : Double and Triple Integrals.

When I tried to connect these topics, I found the same answer : Volume.

My question is how to decide on the method to use? Thank you!

 

[Whovian]

You can actually use multivariable calculus to prove the volume identities in single variable. If we don't have a simple rotation of a two-dimensional object, then we resort to multivariable, otherwise, it's simpler to use the single variable methods, thought it takes more effort to remember and they're just special cases of the multivariable method.

 

[thushanthan]

thanks!