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 Round

 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

 0 n t t n 2 2 /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] FormBox RowBox RowBox RowBox SubsuperscriptBox 0 n RowBox ErrorBox RowBox ⌊t⌉ RowBox t FractionBox SuperscriptBox n 2 2 /; RowBox n TagBox Function TraditionalForm [/itex]

 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