Can one integrate over a discontinuity due to a piecewise function?

Question

anonymous · Answer

$$f(x)=\left[\begin{matrix}1/x &  x<10 \ 0 & x \ge 10\end{matrix}\right]$$

anonymous · Answer

Can one integrate $$\int\limits_{1}^{10}f(x)dx$$

anonymous · Answer

no

anonymous · Answer

Yes no problem whatsoever - area keeps accumulating just fine after the jump. Seriously though integration is a non-local operation and the Rieman sums converge all the same as long as one does not have infinity somewhere.

anonymous · Answer

There are even functions with INFINITE number of jumps that are completely integrable in every interval

anonymous · Answer

lool up "integration with discontinuities" in google or may be even utube

anonymous · Answer

Ah , and dont forget to medal the answer. Thx in advance

anonymous · Answer

I was just think that the upper end for integration ends ON the discontinuous point, that's what's causing me trouble now

anonymous · Answer

Soo - what seems to be the problem? You always MUST COMPUTE such jumps in "pieces" i.e. you integrate as usual up-to the jump and as-usual from the jump and rightward

anonymous · Answer

so the answer to my integral would be: $$\ln 10 $$

anonymous · Answer

y

anonymous · Answer

mdl plz

anonymous · Answer

Noo it is the opposite (Unkle)

anonymous · Answer

thx

zzr0ck3r · Answer

lol

unklerhaukus · Answer

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