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Thread: Need help on "Volume by Cylindrical Shells"

  1. #1
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    Question Need help on "Volume by Cylindrical Shells"

    I have this question due, but I don't know how to solve it. Can someone please help me?

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  2. #2
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    Re: Need help on "Volume by Cylindrical Shells"

    What have you tried?

    (a) Let's set it up. We are using volume by cylindrical shell. So, the volume is:

    $\displaystyle V = \int_0^a 2\pi x y dx = \int_0^a 2\pi xf(x) dx$

    Then the hint is $u =y= f(x), du = f'(x)dx = -xf(x)dx = -xudx$

    So, $-xdx = \dfrac{du}{u}$ gives:

    $\displaystyle V = \int_{f(0)}^{f(a)} -2\pi du = 2\pi \int_{f(a)}^1 du = 2\pi (1-f(a))$

    (b) the diameter is 2a. So, if a approaches infinity, so too does 2a.

    (c) As a approaches infinity, the volume approaches $2\pi$, as $f(a)$ approaches zero.
    Last edited by SlipEternal; Mar 1st 2018 at 08:38 AM.
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