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Homework Help: Iterated integral clarification

  1. Mar 16, 2009 #1
    There is an iterated integral:

    outer integration = 1 to -1 (limits of int.)
    inner integration = sqrt(1-x^2) to -sqrt(1-x^2)
    function = x^2 + y^2

    the part i dont get is the question states to sketch or describe the region, im good with that, but i dont understand what is meant by the following:

    What region in the plane comprises the lower boundary of this region?

    Can anyone help?
  2. jcsd
  3. Mar 16, 2009 #2


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    Hi Derill03! :smile:

    I agree it's a strange question :confused:

    the boundary of a region in the plane is a curve, not a region …

    I suppose it's asking for the bottom half of the circle.
  4. Mar 19, 2009 #3
    Hello Derill03

    I believe I am faced with the same question as you.

    My question is what the graph of this would look like in R3. Is it an inverted conical shape or a sphere?

    The lower boundary that TinyTim was mentioning, "lower half of the circle", is this referring a lower half of a sphere?
  5. Mar 19, 2009 #4


    Staff: Mentor

    No, it's the lower half of a circle in the x-y plane. We're talking about the region over which (double) integration takes place, so this region is two-dimensional. OTOH, the integral itself might represent the volume of a 3D object whose z-value is x^2 + y^2, which is a cone.

    You listed the limits of integration as
    The usual practice is to list the lower limit first, and then the upper limit, not the other way round, as you seem to have done.
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