# 4x^2-1

Input |
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4 x^2 – 1 |

Geometric figure |

parabola |

Alternate form |

(2 x – 1) (2 x + 1) |

Polynomial discriminant |

Delta = 16 |

Derivative |

d/dx(4 x^2 – 1) = 8 x |

Indefinite integral |

integral (-1 + 4 x^2) dx = (4 x^3)/3 – x + constant |

Global minimum |

min{4 x^2 – 1} = -1 at x = 0 |

Definite integral |

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

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

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