# 3cos2x

Input |
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3 cos(2 x) |

Roots |

x = (pi n)/2 – pi/4, n element Z |

Series expansion at x=0 |

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

Derivative |

d/dx(3 cos(2 x)) = -6 sin(2 x) |

Indefinite integral |

integral 3 cos(2 x) dx = 3 sin(x) cos(x) + constant |

Global maxima |

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

Definite integral |

integral_0^(pi/4) 3 cos(2 x) dx = 3/2 = 1.5 |

Definite integral mean square |

integral_0^pi (9 cos^2(2 x))/pi dx = 9/2 = 4.5 |