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Day 2, Problem 5
IMC 2004 · Problem 5
Day 2
20 points
11th IMC · Skopje, Macedonia
Statement
Prove that
∫
0
1
∫
0
1
d
x
d
y
x
−
1
+
∣
ln
y
∣
−
1
≤
1.
\int_0^1 \int_0^1 \frac{dx\,dy}{x^{-1} + |\ln y| - 1} \le 1.
∫
0
1
∫
0
1
x
−
1
+
∣
ln
y
∣
−
1
d
x
d
y
≤
1.
Official solution
Reveal
Hidden so you can work on the problem first.
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