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Arnold's Trivium
1991 Arnold's Trivium
18
18
Part of
1991 Arnold's Trivium
Problems
(1)
Problem 18
Source:
7/1/2010
Calculate
∫
⋯
∫
exp
(
−
∑
1
≤
i
≤
j
≤
n
x
i
x
j
)
d
x
1
⋯
d
x
n
\int\cdots\int \exp\left(-\sum_{1\le i\le j\le n}x_ix_j\right)dx_1\cdots dx_n
∫
⋯
∫
exp
(
−
1
≤
i
≤
j
≤
n
∑
x
i
x
j
)
d
x
1
⋯
d
x
n
integration
linear algebra
matrix
quadratics
Gauss
calculus