{
  "aliases": [
    "primitive-function"
  ],
  "backlinks": [
    {
      "field": "uses",
      "target": "03VHANA6ZK"
    },
    {
      "field": "uses",
      "target": "0NC2A3HWGT"
    },
    {
      "field": "uses",
      "target": "0NHGY0N0JB"
    }
  ],
  "body": "\n## Definition\n\nLet $I$ be an open interval and let $f \\colon I \\to \\mathbb{R}$.\nA function $F \\colon I \\to \\mathbb{R}$ is an antiderivative of $f$ on $I$ if $F$ is differentiable on $I$ and $F'(x) = f(x)$ for all $x \\in I$.\n\n## Remarks\n\nIf $F$ is an antiderivative of $f$, then so is $F + C$ for each constant $C$.\nOn an interval, these are all the antiderivatives, because a function with [[zero derivative|003QDZ4T16]] is constant.\nFor example, $x^3/3$ is an antiderivative of $x^2$ on $\\mathbb{R}$.\nA function with a jump has no antiderivative on an interval, by [[Darboux's theorem|0Q5A47J48D]].\n\n## Explanations\n\n### L1 human\n\nAn antiderivative undoes differentiation.\nWe look for a function whose derivative is the given function.\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "aliases": [
      "primitive-function"
    ],
    "defines": "0BYWRWFT4F",
    "kind": "definition",
    "msc": [
      "26A36"
    ],
    "name": "Antiderivative",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Antiderivative"
      }
    ],
    "tag": "0BW9N5CDSB",
    "uses": [
      "0F1WR9C83K"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0BW9N5CDSB/",
  "links": [
    {
      "field": "defines",
      "target": "0BYWRWFT4F"
    },
    {
      "field": "uses",
      "target": "0F1WR9C83K"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0BW9N5CDSB.md",
  "msc": [
    "26A36"
  ],
  "name": "Antiderivative",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0BW/0BW9N5CDSB.md",
  "status": null,
  "tag": "0BW9N5CDSB",
  "uri": "m2://0BW9N5CDSB",
  "url": "https://math2.tamnd.com/wiki/antiderivative-definition/",
  "writing": {
    "tag": "0BW9N5CDSB",
    "kind": "definition",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}