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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
100
100
Part of
2006 Today's Calculation Of Integral
Problems
(1)
Today's calculation of integral 100
Source: created by kunny
3/30/2006
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive numbers such that
a
b
c
=
1
16
.
abc=\frac{1}{16}.
ab
c
=
16
1
.
Prove the following inequality.
∫
0
∞
x
2
(
x
2
+
a
2
)
(
x
2
+
b
2
)
(
x
2
+
c
2
)
d
x
≤
π
.
\int_0^{\infty} \frac{x^2}{(x^2+a^2)(x^2+b^2)(x^2+c^2)}\ dx\leq \pi.
∫
0
∞
(
x
2
+
a
2
)
(
x
2
+
b
2
)
(
x
2
+
c
2
)
x
2
d
x
≤
π
.
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