# 2sin 2x

Input |
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2 sin(2 x) |

Roots |

x = (pi n)/2, n element Z |

Series expansion at x=0 |

4 x – (8 x^3)/3 + (8 x^5)/15 + O(x^6) (Taylor series) |

Derivative |

d/dx(2 sin(2 x)) = 4 cos(2 x) |

Indefinite integral |

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

Global maxima |

max{2 sin(2 x)} = 2 at x = pi n + pi/4 for integer n |

Definite integral over a half-period |

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

Definite integral mean square |

integral_0^pi (4 sin^2(2 x))/pi dx = 2 |