{
  "icon" : "chart.xyaxis.line",
  "id" : "7BEA2780-73CD-5379-AB3E-727470B19EF7",
  "lines" : [
    {
      "id" : "18F2E7D2-A878-5B15-8DB9-015AF1072214",
      "source" : "# Area between curves"
    },
    {
      "id" : "580A7FD5-CDB3-5D50-83CC-E5AEFABB3189",
      "source" : "\/\/ Between y = x and y = x²."
    },
    {
      "id" : "1B415158-C4B7-5D06-9EC9-D5B4B65A1AAB",
      "source" : "area between = integral(x - x², x, 0, 1)"
    },
    {
      "id" : "90D6149F-C114-500D-95BF-9A2B83896364",
      "source" : "area between == 1\/6"
    },
    {
      "id" : "544B1C66-1933-5375-92C2-05F39071B40D",
      "source" : ""
    },
    {
      "id" : "32C34CC0-28C0-53E2-B718-F391C2DEA36F",
      "source" : "# Average value"
    },
    {
      "id" : "369D88CC-C5CB-5808-B997-E380EAF00CB4",
      "source" : "\/\/ Average of f(x) = x² over 0 to 3."
    },
    {
      "id" : "E7ADCDAF-F427-5434-8210-757A2C244055",
      "source" : "average value = integral(x², x, 0, 3)\/3"
    },
    {
      "id" : "911978AD-3E21-58F5-A85A-4A7E79916B5E",
      "source" : "average value == 3"
    },
    {
      "id" : "CF3364CD-743F-5EA8-9343-36D977629906",
      "source" : ""
    },
    {
      "id" : "F0E64087-92BB-5999-8ACC-6A76E955A4AE",
      "source" : "# Volume of revolution"
    },
    {
      "id" : "A3C00D97-0965-5E58-8349-D2F610861472",
      "source" : "\/\/ Rotating y = √x around the x axis, 0 to 4."
    },
    {
      "id" : "AE73E82B-1BBD-50D4-B291-106620D41F5C",
      "source" : "volume = integral(pi*(sqrt(x))², x, 0, 4)"
    },
    {
      "id" : "A2FD65F6-318D-5394-81AA-B6E276D7BCD0",
      "source" : "volume == 8*pi"
    }
  ],
  "numberStyle" : {
    "decimal" : ".",
    "grouping" : ",",
    "secondaryGroupSize" : 3
  },
  "title" : "Applications of integration"
}