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Basic Integral calculus volume problem

  1. Nov 7, 2007 #1
    Hi everyone, this is my first time posting on these forums. If I am doing anything wrong, please let me know.

    I am having a lot of trouble with conceptualizing rotating lines around the X- and Y-axis.

    The problem I am trying to visualize right now is...

    Using integrals to represent the volume of the solid formed by...

    Y = sqrt(x)+3, Y = 7 - (1/2)x, and the Y-axis. Rotated around the line Y = 3.

    my gut feeling for this problem is...

    To setup the integral so that it looks like this...

    setting the two equations equal, and differentiating for X, the integral is from [0,4]

    and this is then my integral setup.

    (Pi(7 - (1/2)x - 3)^2 - Pi(sqrt(x) + 3 - 3)^2)DX

    This creates a washer with outer radius of Pi(4 - 1/2x)^2 and inner radius Pi(x)

    I am pretty new to calculus, and I understand this is a very basic concept.
    I am just looking for some pointers on how to approach these kinds of problems.

    and is this even a correct way to solve this problem?
  2. jcsd
  3. Nov 7, 2007 #2


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    Homework Helper

    If you are new to this stuff, then you are way ahead of the curve. That looks good to me.
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