(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     16758,        368]
NotebookOptionsPosition[     16170,        344]
NotebookOutlinePosition[     16510,        359]
CellTagsIndexPosition[     16467,        356]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"NIntegrate", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"1", "/", 
       RowBox[{"Sqrt", "[", 
        RowBox[{
         RowBox[{"0.274", "*", 
          RowBox[{
           RowBox[{"(", 
            RowBox[{"1", "+", "z"}], ")"}], "^", "3"}]}], "+", "0.726"}], 
        "]"}]}], "/", 
      RowBox[{"(", 
       RowBox[{"1", "+", "z"}], ")"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", "0", ",", "z0"}], "}"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"z0", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.452361361649722*^9, 3.452361437231221*^9}, {
  3.452361508233231*^9, 3.452361508711318*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwV0Hs41PkeB/BxycntFDqkmGb81Gh00WlJJZ/vpi0lbTsz0io6pkUPG0ts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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0.4},
  PlotRange->{{0, 10}, {0.35902730192677657`, 0.9537769626897403}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.452365902669497*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NIntegrate", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"1", "/", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"8", "*", 
        RowBox[{"10", "^", 
         RowBox[{"(", 
          RowBox[{"-", "5"}], ")"}]}], "*", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "+", "z"}], ")"}], "^", "4"}]}], "+", 
       RowBox[{"0.274", "*", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"1", "+", "z"}], ")"}], "^", "3"}]}], "+", "0.763"}], 
      "]"}]}], "/", 
    RowBox[{"(", 
     RowBox[{"1", "+", "z"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"z", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.452361449833181*^9, 3.452361451085021*^9}, {
  3.4523660288045063`*^9, 3.452366035770008*^9}}],

Cell[BoxData["0.9802067829682304`"], "Output",
 CellChangeTimes->{3.452365965717247*^9, 3.452366037519187*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"5", "*", 
     RowBox[{"Log10", "[", 
      RowBox[{"3", "*", 
       RowBox[{
        RowBox[{"10", "^", "5"}], "/", "70"}], "*", 
       RowBox[{"10", "^", "6"}], "*", 
       RowBox[{"NIntegrate", "[", 
        RowBox[{
         RowBox[{"1", "/", 
          RowBox[{"Sqrt", "[", 
           RowBox[{
            RowBox[{"8", "*", 
             RowBox[{
              RowBox[{"10", "^", 
               RowBox[{"(", 
                RowBox[{"-", "5"}], ")"}]}], "/", 
              RowBox[{"r", "^", "2"}]}]}], "+", 
            RowBox[{"0.274", "/", "r"}], "+", 
            RowBox[{"0.726", "*", 
             RowBox[{"r", "^", "2"}]}]}], "]"}]}], ",", 
         RowBox[{"{", 
          RowBox[{"r", ",", 
           RowBox[{"1", "/", 
            RowBox[{"(", 
             RowBox[{"1", "+", "z"}], ")"}]}], ",", "1"}], "}"}]}], "]"}]}], 
      "]"}]}], "+", 
    RowBox[{"5", "*", 
     RowBox[{"Log10", "[", 
      RowBox[{"1", "+", "z"}], "]"}]}], "-", "5"}], ",", 
   RowBox[{"{", 
    RowBox[{"z", ",", "0.01", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.45236147606664*^9, 3.45236158437878*^9}, {
  3.45236161550185*^9, 3.452361656673539*^9}, {3.452387337241811*^9, 
  3.452387362287759*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVz2k4lYsWB/B9k1MpqURKKFwZSpkOZVjrffd+y5Ah06lIUYoIITKkUkgD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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 34.},
  PlotRange->{{0.01, 1}, {33.166355861124664`, 43.40651062292856}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.452387377461874*^9},
 ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"]]
}, Open  ]]
},
WindowSize->{644, 462},
WindowMargins->{{11, Automatic}, {Automatic, 25}},
FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (November 10, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 699, 21, 43, "Input"],
Cell[1269, 45, 2686, 50, 232, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3992, 100, 787, 24, 43, "Input"],
Cell[4782, 126, 110, 1, 27, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4929, 132, 1292, 37, 88, "Input"],
Cell[6224, 171, 9930, 170, 232, 3258, 59, "CachedBoxData", "BoxData", "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)