# 2sinxcosx=

Input |
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2 sin(x) cos(x) |

Roots |

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

Series expansion at x=0 |

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

Derivative |

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

Indefinite integral |

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

Definite integral over a half-period |

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

Definite integral mean square |

integral_0^pi (4 cos^2(x) sin^2(x))/pi dx = 1/2 = 0.5 |