# 1+2cosx

Input |
---|

1 + 2 cos(x) |

Alternate form |

e^(-i x) + e^(i x) + 1 |

Series expansion at x=0 |

3 – x^2 + x^4/12 + O(x^6) (Taylor series) |

Derivative |

d/dx(1 + 2 cos(x)) = -2 sin(x) |

Indefinite integral |

integral (1 + 2 cos(x)) dx = x + 2 sin(x) + constant |

Global maxima |

max{1 + 2 cos(x)} = 3 at x = 2 pi n for integer n |

Definite integral over a half-period |

integral_0^pi (1 + 2 cos(x)) dx = pi~~3.14159 |

Definite integral over a period |

integral_0^(2 pi) (1 + 2 cos(x)) dx = 2 pi~~6.28319 |

Definite integral mean square |

integral_0^(2 pi) (1 + 2 cos(x))^2/(2 pi) dx = 3 |