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variants of this functions
DiracDelta




Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/14.03.21.0001.02









  


  








Input Form





Integrate[DiracDelta[x], x] == HeavisideTheta[x]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], RowBox[List["\[DifferentialD]", "x"]]]]]], "\[Equal]", RowBox[List["HeavisideTheta", "[", "x", "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> x </mi> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> HeavisideTheta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> x </ci> </bvar> <apply> <ci> DiracDelta </ci> <ci> x </ci> </apply> </apply> <apply> <ci> HeavisideTheta </ci> <ci> x </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["DiracDelta", "[", "x_", "]"]], RowBox[List["\[DifferentialD]", "x_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["HeavisideTheta", "[", "x", "]"]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29