andrew123 | can anyone integrate using substitution: sin[(sqrt)x] / (sqrt)x |

Safrole | u = sqrt(x), so du = 1/(2sqrt(x)) dx |

Copter2 | looks like a sin there though :o |

Safrole | thus we get int( sin(sqrt(x))/sqrt(x) dx ) = 2*int( sin(u) du ) = -2cos(u) = -2cos(sqrt(x)) |

TheBlueWizard | equivalently, x = u^2, dx = 2 u du, and then substituting is pretty straightforward |

[n01d] | hi guys, whats the function/algorithm to calcalculate sine? |

andrew123 | safrole: if u = sqrt(x) wudnt we get sinu/u du |

Safrole | if u = sqrt(x) then du = 1/(2sqrt(x)) du = 1/(2sqrt(x)) dx, sorry so then 2 du = 1/sqrt(x) dx so then we get int( sin(sqrt(x))/sqrt(x) dx ) = int( sin(u) du ) = 2*int( sin(u) du ) sorry I forgot the 2 |

andrew123 | but we are integrating in regards to u.. so dont we need du/dx = 1/2sqrt(x) then dx = 2sqrt(x).du |

Safrole | andrew you're mixing things here that need nod be mixed we want a substitution for 1/sqrt(x) dx I found one |

bsmntbombdood | is >, < defined on C? |

Safrole | < . > you mean? An inner product? |

[n01d] | can someone help me whats the manual to solve sine. not using calculator |

bsmntbombdood | no, greater/less than |

Safrole | C is *not* an ordered field |

Eclipsor | [n01d]: ? |

Safrole | you can impose a so called lexicographical order |

Eclipsor | solve sine in what way |

Safrole | but that still has some nuances But in general, no > and < are not defined for C |

shinygerbil | [n01d]: do you mean like the Taylor series of sin(x)? |

bsmntbombdood | ok |

Safrole | the Taylor series would require knowledge of cosine |

shinygerbil | hehe, true |

Safrole | that's kind of circular. |

bsmntbombdood | Safrole: no it wouldn't |

shinygerbil | no, wait well, kinda |

bsmntbombdood | cos(0) is easy to find |

shinygerbil | actually doing a Taylor expansion on sin(x) would |