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Arnold's Trivium
1991 Arnold's Trivium
65
Problem 65
Problem 65
Source:
July 1, 2010
function
logarithms
algebra
domain
integration
geometry
3D geometry
Problem Statement
Find the mean value of the function
ln
r
\ln r
ln
r
on the circle
(
x
−
a
)
2
+
(
y
−
b
)
2
=
R
2
(x - a)^2 + (y-b)^2 = R^2
(
x
−
a
)
2
+
(
y
−
b
)
2
=
R
2
(of the function
1
/
r
1/r
1/
r
on the sphere).
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