(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 2284, 76] NotebookOptionsPosition[ 2030, 63] NotebookOutlinePosition[ 2374, 78] CellTagsIndexPosition[ 2331, 75] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[{"\"\< 15.1 #14 \>\"", "\[IndentingNewLine]", RowBox[{"Integrate", "[", " ", RowBox[{ RowBox[{"x", "*", RowBox[{"y", "/", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"y", "^", "2"}], "+", "1"}], "]"}]}]}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"y", ",", "0", ",", "1"}], "}"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"NIntegrate", "[", " ", RowBox[{ RowBox[{"x", "*", RowBox[{"y", "/", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"y", "^", "2"}], "+", "1"}], "]"}]}]}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"y", ",", "0", ",", "1"}], "}"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"RegionPlot3D", "[", RowBox[{ RowBox[{"z", "\[LessEqual]", " ", RowBox[{"x", "*", RowBox[{"y", "/", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"x", "^", "2"}], "+", RowBox[{"y", "^", "2"}], "+", "1"}], "]"}]}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"z", ",", "0", ",", "0.6"}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.47023767234375*^9, 3.4702377646875*^9}, { 3.470239372671875*^9, 3.47023940665625*^9}}] }, WindowSize->{1189, 837}, WindowMargins->{{Automatic, 6}, {Automatic, 5}}, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 1481, 41, 92, "Input"] } ] *) (* End of internal cache information *)