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Math Help - [SOLVED] find volume..

  1. #1
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    [SOLVED] find volume..

    i cannot figure this out for the life of me.. find the volume of these functions using disk method:


    y^2= x , x = 2y ; flip about the y - axis...

    answer is 64pie/15


    i m sure not getting that..
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Legendsn3verdie View Post
    i cannot figure this out for the life of me.. find the follow of these functions using disk method:


    y^2= x , x = 2y ; flip about the y - axis...

    answer is 64pie/15


    i m sure not getting that..
    look up the disk method, and make sure you understand how i set up the integral below

    the volume is given by V = \pi \int_0^2 [(2y)^2 - (y^2)^2]~dy
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  3. #3
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    So the area in question is the area bounded by the two curves x = y^2; x = 2y and rotated around the y-axis. You can solve this by using washers or cylinders. If you use washers, the integral will be \int _0 ^2 \pi(4y^2 - y^4) dy.
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  5. #5
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    Just for fun, let's do it with shells and see if we get the same thing.

    2{\pi}\int_{0}^{4}x\left(\sqrt{x}-\frac{x}{2}\right)dx

    Also, from now on, anyone caught spelling 'pi' as
    'pie' will be sent to a work camp.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by galactus View Post
    Also, from now on, anyone caught spelling 'pi' as
    'pie' will be sent to a work camp.
    haha, i caught that too. but i couldn't be bothered to point it out...yet again
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