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Mathematics
Mathematics
Problem
For a differentiable function
f
f
f
, let
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
g(x) = \int_{0}^{x} f(t)\,dt
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
. If
g
(
6
)
=
15
g(6)=15
g
(
6
)
=
15
, determine the average value of
f
f
f
on the interval
[
0
,
6
]
[0,6]
[
0
,
6
]
.
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