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What is the region this question is decribing ?

  1. Jan 27, 2013 #1
    Yeah, so this might sound like a dumb question, but I'm going to ask anyway!

    "Find the volume of the solid generated by revolving the described region about the given axis:

    The region enclosed above by the curve y= 1 + (x^2/4), below by the x-axis, to the left by the y-axis, and to the right by the line x=3, rotated about the y-axis."

    I can easily find the region the question is talking about when it says that it's bound by this or that curve.
    But I'm confused here.

    The curve, y= 1 + x2/4, is above the x-axis.
    So how can we have another boundary that's "below the x-axis" when it also has to be above y= 1 + x2/4??? :confused: ugh.

    And how can the same region be to the left of the y-axis and also to the right of x=3?

    This makes no sense to me. I thought there was supposed to be some region bounded by the curves that gets rotated around the y-axis!

    How do I solve this sort of problem?

    Thanks so much for helping! :)
  2. jcsd
  3. Jan 27, 2013 #2


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    Science Advisor
    Homework Helper

    I think your problem is understanding the English. The sentence splits up like this:

    The region enclosed (bounded) above by the curve y= 1 + (x^2/4),
    and enclosed below by the x-axis,
    and enclosed to the left by the y-axis,
    and enclosed to the right by the line x=3, rotated about the y-axis.

    "Enclosed below by the x axis" means "the x axis is the lower boundary", not "the region is below the x axis".
    "Enclosed to the left by the y-axis" means "the y axis is the left boundary", etc.
  4. Jan 27, 2013 #3
    OH, HA! I get it now! I wasn't reading it right! ;) Thanks! :D
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