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Meaning of partial differential in limits of integration?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)For Green's theorem, why is the region of integration of the line integral a weird partial derivative character?Understanding Limits of Integration in Integration-by-PartsPartial limits of sequencesReversing the limits of an integrationWhen may we ignore the limits of integration?differentiation integral symbolLimits of definite integralChanging signs of integration limitsChange of limits of integrationIntegration by substitution as the chain rule for integrationMethods to determine integration limits?










0












$begingroup$


I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_partial z $



What exactly does it represent/mean? When is it used?










share|cite|improve this question









$endgroup$







  • 1




    $begingroup$
    It might be the boundary of some domain.
    $endgroup$
    – Gibbs
    Mar 26 at 10:14











  • $begingroup$
    ohh...ok... i get it... Q is a region that denotes an "area", whereas $partialQ$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
    $endgroup$
    – DiscreteMath
    Mar 28 at 15:26
















0












$begingroup$


I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_partial z $



What exactly does it represent/mean? When is it used?










share|cite|improve this question









$endgroup$







  • 1




    $begingroup$
    It might be the boundary of some domain.
    $endgroup$
    – Gibbs
    Mar 26 at 10:14











  • $begingroup$
    ohh...ok... i get it... Q is a region that denotes an "area", whereas $partialQ$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
    $endgroup$
    – DiscreteMath
    Mar 28 at 15:26














0












0








0





$begingroup$


I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_partial z $



What exactly does it represent/mean? When is it used?










share|cite|improve this question









$endgroup$




I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_partial z $



What exactly does it represent/mean? When is it used?







calculus integration definite-integrals






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 26 at 10:13









Simplex1Simplex1

745




745







  • 1




    $begingroup$
    It might be the boundary of some domain.
    $endgroup$
    – Gibbs
    Mar 26 at 10:14











  • $begingroup$
    ohh...ok... i get it... Q is a region that denotes an "area", whereas $partialQ$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
    $endgroup$
    – DiscreteMath
    Mar 28 at 15:26













  • 1




    $begingroup$
    It might be the boundary of some domain.
    $endgroup$
    – Gibbs
    Mar 26 at 10:14











  • $begingroup$
    ohh...ok... i get it... Q is a region that denotes an "area", whereas $partialQ$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
    $endgroup$
    – DiscreteMath
    Mar 28 at 15:26








1




1




$begingroup$
It might be the boundary of some domain.
$endgroup$
– Gibbs
Mar 26 at 10:14





$begingroup$
It might be the boundary of some domain.
$endgroup$
– Gibbs
Mar 26 at 10:14













$begingroup$
ohh...ok... i get it... Q is a region that denotes an "area", whereas $partialQ$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
$endgroup$
– DiscreteMath
Mar 28 at 15:26





$begingroup$
ohh...ok... i get it... Q is a region that denotes an "area", whereas $partialQ$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
$endgroup$
– DiscreteMath
Mar 28 at 15:26











2 Answers
2






active

oldest

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1












$begingroup$

If you provide more context, it may be clearer but it may mean "the boundary of $z$".



This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.






share|cite|improve this answer









$endgroup$




















    1












    $begingroup$

    The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.






    share|cite|improve this answer









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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      1












      $begingroup$

      If you provide more context, it may be clearer but it may mean "the boundary of $z$".



      This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.






      share|cite|improve this answer









      $endgroup$

















        1












        $begingroup$

        If you provide more context, it may be clearer but it may mean "the boundary of $z$".



        This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.






        share|cite|improve this answer









        $endgroup$















          1












          1








          1





          $begingroup$

          If you provide more context, it may be clearer but it may mean "the boundary of $z$".



          This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.






          share|cite|improve this answer









          $endgroup$



          If you provide more context, it may be clearer but it may mean "the boundary of $z$".



          This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Mar 26 at 10:14









          StackTDStackTD

          24.3k2254




          24.3k2254





















              1












              $begingroup$

              The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.






              share|cite|improve this answer









              $endgroup$

















                1












                $begingroup$

                The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.






                share|cite|improve this answer









                $endgroup$















                  1












                  1








                  1





                  $begingroup$

                  The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.






                  share|cite|improve this answer









                  $endgroup$



                  The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Mar 26 at 10:16









                  5xum5xum

                  92.7k394162




                  92.7k394162



























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