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Vojtěch Jarník IMC
2018 VJIMC
4
Double integral with exponentials
Double integral with exponentials
Source: VJIMC 2018, Category II, Problem 4
April 14, 2018
calculus
integration
Double integral
Problem Statement
Compute the integral
∬
R
2
(
1
−
e
−
x
y
x
y
)
2
e
−
x
2
−
y
2
d
x
d
y
.
\iint_{\mathbb{R}^2} \left(\frac{1-e^{-xy}}{xy}\right)^2 e^{-x^2-y^2} dx dy.
∬
R
2
(
x
y
1
−
e
−
x
y
)
2
e
−
x
2
−
y
2
d
x
d
y
.
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