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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/04.03.21.0004.01









  


  








Input Form





Integrate[Round[t], {t, 0, n}] == n^2/2 /; Element[n, Integers] && n >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "n"], RowBox[List[RowBox[List["Round", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", FractionBox[SuperscriptBox["n", "2"], "2"]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> n </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> <mfrac> <msup> <mi> n </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> &#8747; </ms> <ms> 0 </ms> <ms> n </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> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <ms> n </ms> <ms> 2 </ms> </apply> <ms> 2 </ms> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> &#8712; </ms> <apply> <ci> TagBox </ci> <ms> &#8469; </ms> <apply> <ci> Function </ci> <integers /> </apply> </apply> </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", "n_"], RowBox[List[RowBox[List["Round", "[", "t_", "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["n", "2"], "2"], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2001-10-29