# 4x-x^2

Input |
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4 x – x^2 |

Geometric figure |

parabola |

Polynomial discriminant |

Delta = 16 |

Derivative |

d/dx(4 x – x^2) = 4 – 2 x |

Indefinite integral |

integral (4 x – x^2) dx = 2 x^2 – x^3/3 + constant |

Global maximum |

max{4 x – x^2} = 4 at x = 2 |

Definite integral |

integral_0^4 (4 x – x^2) dx = 32/3~~10.6667 |

Definite integral area above the axis between the smallest and largest real roots |

integral_0^4 (4 x – x^2) theta(4 x – x^2) dx = 32/3~~10.6667 |