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Today's Calculation Of Integral
2012 Today's Calculation Of Integral
843
843
Part of
2012 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 843
Source: created by kunny
8/22/2012
Let
f
(
x
)
f(x)
f
(
x
)
be a continuous function such that
∫
0
1
f
(
x
)
d
x
=
1.
\int_0^1 f(x)\ dx=1.
∫
0
1
f
(
x
)
d
x
=
1.
Find
f
(
x
)
f(x)
f
(
x
)
for which
∫
0
1
(
x
2
+
x
+
1
)
f
(
x
)
2
d
x
\int_0^1 (x^2+x+1)f(x)^2dx
∫
0
1
(
x
2
+
x
+
1
)
f
(
x
)
2
d
x
is minimized.
calculus
integration
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inequalities
special factorizations
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