given a function [itex]f(x)[/itex] that is piecewise smooth on interval [itex]-L<x<L[/itex] except at [itex]N-1[/itex] points, is [itex]\int_{-L}^L f'(x)dx [/itex] legal or would i have to [tex]\sum_{i=1}^N \int_{x_i}^{x_{i+1}} f'(x)dx[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where [itex]x_{N+1}=L[/itex] and [itex]x_{1}=-L[/itex]

also, am i correct that if [itex]f(x)[/itex] is piecewise smooth, then [itex]f'(x)[/itex] is piecewise continuous but not necessarily piecewise smooth?

thanks in advance!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integrating over piecewise functions

Loading...

Similar Threads - Integrating piecewise functions | Date |
---|---|

I Solving an integral | Monday at 4:38 PM |

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus | Saturday at 12:51 PM |

A Integrate f(x) = tanh(c*x^b)? Wolfram says not possible ... | Mar 11, 2018 |

I Looking for additional material about limits and distributions | Feb 17, 2018 |

A Inverse Laplace transform of a piecewise defined function | Feb 17, 2017 |

**Physics Forums - The Fusion of Science and Community**