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Integrals over different domains

  1. Jan 6, 2012 #1
    Folks,

    When we are evaluating integrals like the following, what are we evaluating in terms of units etc.

    For example if I integrate Fdx I get an area which represents the energy where F is the force and d is the displacement so the units are Nm etc.

    1) Integrals over intervals
    ???

    2)Double integrals over 2-D regions

    Is this an area of a 2d surface?


    3)Triple integrals over 3-D solids

    Is this an area of a 3d surface?


    4)Line integrals along curves in 2-D space
    5) Line integrals along curves in 3-D space

    These 2 would not be an area becasue we are dealing with curves?


    6) Integrals over surfaces in 3-D space?

    Is this an area over 3-d surfaces/solids?

    Hopefully some one can can clarify

    I am asking this in the context of geometric surfaces like one would see in calculus books etc.

    Thanks
     
  2. jcsd
  3. Jan 6, 2012 #2

    mathman

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    Science Advisor
    Gold Member

    In all cases it depends on what the integrand is.
     
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