Input |

5 y (2 y – 3) + (2 y – 3) |

Result |

5 (2 y – 3) y + 2 y – 3 |

Geometric figure |

parabola |

Polynomial discriminant |

Delta = 289 |

Derivative |

d/dy(5 y (2 y – 3) + (2 y – 3)) = 20 y – 13 |

Indefinite integral |

integral (-3 + 2 y + 5 y (-3 + 2 y)) dy = (10 y^3)/3 – (13 y^2)/2 – 3 y + constant |

Global minimum |

min{5 y (2 y – 3) + (2 y – 3)} = -289/40 at y = 13/20 |

Definite integral |

integral_(-1/5)^(3/2) (-3 + 2 y + 5 y (-3 + 2 y)) dy = -4913/600~~-8.18833 |

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

integral_(-1/5)^(3/2) (-3 + 2 y + 5 y (-3 + 2 y)) theta(3 – 2 y – 5 y (-3 + 2 y)) dy = -4913/600~~-8.18833 |