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Mathematics
Problem
For the function
f
(
x
)
=
1
x
2
f(x)=\dfrac{1}{x^{2}}
f
(
x
)
=
x
2
1
defined on the interval
[
a
,
4
]
[a,4]
[
a
,
4
]
with
a
<
4
a<4
a
<
4
, the average value of
f
f
f
over this interval is
1
6
\dfrac16
6
1
. Determine the value of
a
.
a\,.
a
.
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