# 6sinx

Input |
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6 sin(x) |

Alternate form |

3 i e^(-i x) – 3 i e^(i x) |

Roots |

x = pi n, n element Z |

Series expansion at x=0 |

6 x – x^3 + x^5/20 + O(x^6) (Taylor series) |

Derivative |

d/dx(6 sin(x)) = 6 cos(x) |

Indefinite integral |

integral 6 sin(x) dx = -6 cos(x) + constant |

Global maxima |

max{6 sin(x)} = 6 at x = 2 pi n + pi/2 for integer n |

Definite integral over a half-period |

integral_0^pi 6 sin(x) dx = 12 |

Definite integral mean square |

integral_0^(2 pi) (18 sin^2(x))/pi dx = 18 |