# Cosx * sinx

Input |
---|

cos(x) sin(x) |

Series expansion at x=0 |

x – (2 x^3)/3 + (2 x^5)/15 + O(x^6) (Taylor series) |

Derivative |

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

Indefinite integral |

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

Definite integral over a half-period |

integral_0^(pi/2) cos(x) sin(x) dx = 1/2 = 0.5 |

Definite integral mean square |

integral_0^pi (cos^2(x) sin^2(x))/pi dx = 1/8 = 0.125 |