Matematické Fórum

stuart clark · 18. 12. 2011 13:38

$\int_{0}^{3} (x^2+1)d(\left[x\right])$

where $\left[x\right]=$ greatest Integer function

vanok · 18. 12. 2011 17:13

Hi ↑ stuart clark:,
How as it is defined d([x])?
Thank you.

stuart clark · 20. 12. 2011 12:01

but answer given is $=17$

which is describe as $\sum_{x=1}^{3}(x^2+1).1 = 17$

vanok can you explain me the last line

Thanks

Pavel · 20. 12. 2011 16:08

↑ vanok:

This integral can be calculated in the sense of Riemann–Stieltjes integral, see here. You can find here the meaning of the symbol $\text{d}([x])$

vanok · 20. 12. 2011 19:54

Hi ↑ Pavel:,
Thank you very much.
I also thought that it is about Riemann–Stieltjes integral.
However the notation $\text{d}([x])$ is unknown for me.

check_drummer · 20. 12. 2011 20:51

↑ vanok:
I think the notation $\text{d}([x])$ is special case of the notation mentioned by ↑ Pavel: where we have $g(x):=[x]$ .

vanok · 20. 12. 2011 21:51

↑ check_drummer:;
Thank you very much

Matematické Fórum

#1 18. 12. 2011 13:38

integral with floor function

#2 18. 12. 2011 17:13

Re: integral with floor function

#3 20. 12. 2011 12:01

Re: integral with floor function

#4 20. 12. 2011 16:08

Re: integral with floor function

#5 20. 12. 2011 19:54

Re: integral with floor function

#6 20. 12. 2011 20:51

Re: integral with floor function

#7 20. 12. 2011 21:51

Re: integral with floor function

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