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Round




Mathematica Notation

Traditional Notation









Integer Functions > Round[z] > Integration > Definite integration > For the direct function itself





http://functions.wolfram.com/04.03.21.0005.01









  


  








Input Form





Integrate[Round[t], {t, 0, a}] == (1/2) (2 a - Round[a]) Round[a]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "a"], RowBox[List[RowBox[List["Round", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["Round", "[", "a", "]"]]]], ")"]], " ", RowBox[List["Round", "[", "a", "]"]]]]]]]]








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> <mn> 0 </mn> <mi> a </mi> </msubsup> <mrow> <mrow> <mo> &#8970; </mo> <mi> t </mi> <mo> &#8969; </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8970; </mo> <mi> a </mi> <mo> &#8969; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8970; </mo> <mi> a </mi> <mo> &#8969; </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> &#8747; </ms> <ms> 0 </ms> <ms> a </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> ErrorBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#8970;t&#8969; </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#8518; </ms> <ms> t </ms> </list> </apply> </list> </apply> </list> </apply> <ms> &#10869; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> 2 </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> a </ms> </list> </apply> <ms> - </ms> <ms> &#8970;a&#8969; </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> &#8201; </ms> <ms> &#8970;a&#8969; </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "a_"], RowBox[List[RowBox[List["Round", "[", "t_", "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["Round", "[", "a", "]"]]]], ")"]], " ", RowBox[List["Round", "[", "a", "]"]]]]]]]]


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





2001-10-29