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Math Help - Volume through washer with integration*cough* Calculus 1

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    Newbie ILovePizza's Avatar
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    Question Volume through washer with integration*cough* Calculus 1

    Find the volume of the solid obtained by ratating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

    y = x^4, y = 1; about y = 2

    I get that it's a parabola bounded by y = 1... I see that on my graph. And then it's supposed to rotate forward about the x-axis, not sideways right?

    But y = 2? So it's 2 unit's shifted upward?

    I can't figure this out. Need some

    ???
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  2. #2
    MHF Contributor
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    Re: Volume through washer with integration*cough* Calculus 1

    No, it's not a parabola. It's a quartic...
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    Re: Volume through washer with integration*cough* Calculus 1

    The problem says that you're rotating about y=2. So your washer has an inner radius of 1 and an outer radius of 2-x^4. So you integrate from x=-1 to x=1, pi times (outer radius squared - inner radius squared) dx.

    - Hollywood
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    Newbie ILovePizza's Avatar
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    Cool Re: Volume through washer with integration*cough* Calculus 1

    Okay. I was making arithmetic mistakes, woops xD

    Thanks
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    Re: Volume through washer with integration*cough* Calculus 1

    Quote Originally Posted by ILovePizza View Post
    Okay. I was making arithmetic mistakes, woops xD

    Thanks
    That's a very strange response. No one said anything about any arithmetic mistakes.
    By the way, since the upper boundary is a horizontal straight line, You can treat it as simplly a disk, from y= 2 to y= x^4.
    Last edited by HallsofIvy; May 13th 2013 at 02:14 PM.
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    Newbie ILovePizza's Avatar
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    Re: Volume through washer with integration*cough* Calculus 1

    I never showed my work. It's strange you said it was a strange response :|
    I had been working on this problem for a long time last night. And was tired by the time I went to sleep. Woke up right now and started working on the problem again. Turns out it was arithmetic mistakes after integrating. I was tired, I couldn't think.

    Thanks though
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