Input |

3 x^2 – 1 |

Geometric figure |

parabola |

Alternate form |

-1/3 (sqrt(3) – 3 x) (3 x + sqrt(3)) |

Polynomial discriminant |

Delta = 12 |

Derivative |

d/dx(3 x^2 – 1) = 6 x |

Indefinite integral |

integral (-1 + 3 x^2) dx = x^3 – x + constant |

Global minimum |

min{3 x^2 – 1} = -1 at x = 0 |

Definite integral |

integral_(-1/sqrt(3))^(1/sqrt(3)) (-1 + 3 x^2) dx = -4/(3 sqrt(3))~~-0.7698 |

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

integral_(-1/sqrt(3))^(1/sqrt(3)) (-1 + 3 x^2) theta(1 – 3 x^2) dx = -4/(3 sqrt(3))~~-0.7698 |