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Results tagged with integration
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user 131653
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
4
votes
2
answers
695
views
Integrate $1/(x_1x_2\cdots x_n)^k$ for $1\le x_i \le a$, where product of coordinates satisf...
I need to integrate
$$
\int\limits_{[1,a]^n} \frac {\chi(\{ b \le x_1 \cdots x_n \le c \})} {( x_1 x_2 \cdots x_n)^k} \,dx_1 \cdots dx_n,
$$ where $\chi(E)$ is the characteristic function of a set $E$ …
- 91
1
vote
Integrate $1/(x_1x_2\cdots x_n)^k$ for $1\le x_i \le a$, where product of coordinates satisf...
To expand on the excellent comments and answers provided here and following up on Terry Tao's proposition to take the Fourier expansion of the indicator function in the integral, I derived an alternat …
- 91