# 4x^2+4x

Input |
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4 x^2 + 4 x |

Geometric figure |

parabola |

Polynomial discriminant |

Delta = 16 |

Derivative |

d/dx(4 x^2 + 4 x) = 8 x + 4 |

Indefinite integral |

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

Global minimum |

min{4 x^2 + 4 x} = -1 at x = -1/2 |

Definite integral |

integral_(-1)^0 (4 x + 4 x^2) dx = -2/3~~-0.666667 |

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

integral_(-1)^0 (4 x + 4 x^2) theta(-4 x – 4 x^2) dx = -2/3~~-0.666667 |