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!

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# Integrating over piecewise functions

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