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Math Help - volume problem

  1. #1
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    volume problem

    what is the volume of the region bound by

    y=4/x and y=(x-3)^2 about the y-axis.

    I was trying to use this:

    2pi*INT[ x(4/x)-x(x-3)^2]
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Are you using x = 1 and 4 for your limits of integration?

    If you are submit your work to see where the problem might be--your integrand is correct
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  3. #3
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    yeah, forgot the bounds. intersection is at x=1 and x=4. I must be making an algebraic mistake then.

    4x-(x^4/4-2x^3+9x^2/2)

    evaluated between 4 and 1?
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  4. #4
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    why are you integrating between y= 1 and y= 4? If you draw a graph you will see that parabola y= (x-3)^2 extends down to y= 0. I suggest you do this as two parts: integrate what you have from y= 1 to y= 4 then set up a different integral for the part from y= 0 to y= 1.
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  5. #5
    MHF Contributor Calculus26's Avatar
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    Canadian is using the shell method for rotating about the y axis

    thats why the limits are x= 1 to 4

    Canadian -- 4x-(x^4/4-2x^3+9x^2/2) is correct
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  6. #6
    MHF Contributor Calculus26's Avatar
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    you should get 27pi/2
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