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variants of this functions
UnitStep




Mathematica Notation

Traditional Notation









Generalized Functions > UnitStep[x] > Integration > Definite integration





http://functions.wolfram.com/14.01.21.0004.01









  


  








Input Form





Integrate[UnitStep[t] UnitStep[x - t], {t, -Infinity, Infinity}] == x UnitStep[x]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "\[Infinity]"], RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", "t", "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List["x", "-", "t"]], "]"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List["x", " ", RowBox[List["UnitStep", "[", "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> <msubsup> <mo> &#8747; </mo> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mi> &#8734; </mi> </msubsup> <mrow> <mrow> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> x </mi> <mo> - </mo> <mi> t </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> UnitStep </ci> <ci> t </ci> </apply> <apply> <ci> UnitStep </ci> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> x </ci> <apply> <ci> UnitStep </ci> <ci> x </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "\[Infinity]"], RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", "t_", "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List["x_", "-", "t_"]], "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["x", " ", RowBox[List["UnitStep", "[", "x", "]"]]]]]]]]


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





2007-05-02