MathDB
Problems
Contests
National and Regional Contests
Romania Contests
District Olympiad
2012 District Olympiad
1
Romania District Olympiad 2012 - Grade XII
Romania District Olympiad 2012 - Grade XII
Source:
March 10, 2012
limit
integration
calculus
real analysis
real analysis unsolved
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
three positive distinct real numbers. Evaluate:
lim
t
→
∞
∫
0
t
1
(
x
2
+
a
2
)
(
x
2
+
b
2
)
(
x
2
+
c
2
)
d
x
\lim_{t\to \infty} \int_0^t \frac{1}{(x^2+a^2)(x^2+b^2)(x^2+c^2)}dx
t
→
∞
lim
∫
0
t
(
x
2
+
a
2
)
(
x
2
+
b
2
)
(
x
2
+
c
2
)
1
d
x
Back to Problems
View on AoPS