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South Korea USCM
2018 Korea USCM
3
3
Part of
2018 Korea USCM
Problems
(1)
Maximum value of Integral on subset of plane
Source: 2018 South Korea USCM P3
8/14/2020
Φ
\Phi
Φ
is a function defined on collection of bounded measurable subsets of
R
\mathbb{R}
R
defined as
Φ
(
S
)
=
∬
S
(
1
−
5
x
2
+
4
x
y
−
5
y
2
)
d
x
d
y
\Phi(S) = \iint_S (1-5x^2 + 4xy-5y^2 ) dx dy
Φ
(
S
)
=
∬
S
(
1
−
5
x
2
+
4
x
y
−
5
y
2
)
d
x
d
y
Find the maximum value of
Φ
\Phi
Φ
.
calculus
integration
function
college contests