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Homework Help: Question on integrands

  1. May 2, 2012 #1
    I am having trouble understanding or visualizing how the integrand affects the plot of an integral.

    So I know that

    [itex]\int_{0}^{10}\int_{0}^{10}\int_{0}^{10} 1 {dx}{dy}{dz} [/itex]

    will give you the volume of a 10x10x10 cube. I am wondering what exactly you are getting when you integrate some thing like

    [itex]\int_{0}^{10}\int_{0}^{10}\int_{0}^{10} x^2 {dx}{dy}{dz} [/itex]

    or even if the integrand was something like y^2 + z^2

    If it is easier to understand what is happening with a single or double integral then I would be happy with an explanation from that.
  2. jcsd
  3. May 2, 2012 #2


    Staff: Mentor

    You might think of the integrand (1) as a function that gives the density at each point the 3D space. If we attach units to this function, say g/cm3, then the result is the mass of a 10 cm x 10 cm x 10 cm cube whose density is constant.
    You could also think of the integrand here as being a density function define on R3, but the density varies only in the x-direction.
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