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Math Help - volumes of revolution

  1. #1
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    volumes of revolution

    Hello,

    I perfectly understand both methods (discs and shells) my only problem is to know which one to use.


    Let's say I had a problem it would be hard fo me to know which method to use... and would both work each time?


    Thank you
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  2. #2
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    It's more a matter of convenience. There's not a function I can think of that you couldn't weasle through with either method. A torus is a common example where shells are a little more stright forward. This is a good example where washer would be preferred.
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  3. #3
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    Ok thaks so much, so basically both methods work each time but you could have a method which is easier to use!
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  4. #4
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    Quote Originally Posted by thehabsonice View Post
    Ok thaks so much, so basically both methods work each time but you could have a method which is easier to use!
    Usually one method has easier integrations and/or one integral opposed to two integrals. Case in point revolve the region bound by

    y = x, y = 2-x, y = 0 about the y -axis

    Shells: 2 \pi \int_0^1 x\cdot x\,dx + 2 \pi \int_1^2 x(2-x)\,dx
    Washers \pi \int_0^1 (2-y)^2-y^2\, dy
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