Input |

3 x^2 + 5 x – 2 |

Geometric figure |

parabola |

Polynomial discriminant |

Delta = 49 |

Derivative |

d/dx(3 x^2 + 5 x – 2) = 6 x + 5 |

Indefinite integral |

integral (-2 + 5 x + 3 x^2) dx = x^3 + (5 x^2)/2 – 2 x + constant |

Global minimum |

min{3 x^2 + 5 x – 2} = -49/12 at x = -5/6 |

Definite integral |

integral_(-2)^(1/3) (-2 + 5 x + 3 x^2) dx = -343/54~~-6.35185 |

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

integral_(-2)^(1/3) (-2 + 5 x + 3 x^2) theta(2 – 5 x – 3 x^2) dx = -343/54~~-6.35185 |