# 2sin^2x

Input |
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2 sin^2(x) |

Roots |

x = pi n, n element Z |

Series expansion at x=0 |

2 x^2 – (2 x^4)/3 + (4 x^6)/45 – (2 x^8)/315 + O(x^9) (Taylor series) |

Derivative |

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

Indefinite integral |

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

Definite integral over a half-period |

integral_0^(pi/2) 2 sin^2(x) dx = pi/2~~1.5708 |

Definite integral over a period |

integral_0^pi 2 sin^2(x) dx = pi~~3.14159 |

Definite integral mean square |

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