Input |

16 x^4 – 81 |

Alternate form |

(2 x – 3) (2 x + 3) (4 x^2 + 9) |

Polynomial discriminant |

Delta = -557256278016 |

Derivative |

d/dx(16 x^4 – 81) = 64 x^3 |

Indefinite integral |

integral (-81 + 16 x^4) dx = (16 x^5)/5 – 81 x + constant |

Global minimum |

min{16 x^4 – 81} = -81 at x = 0 |

Definite integral |

integral_(-3/2)^(3/2) (-81 + 16 x^4) dx = -972/5 = -194.4 |

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

integral_(-3/2)^(3/2) (-81 + 16 x^4) theta(81 – 16 x^4) dx = -972/5 = -194.4 |