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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
x
f(x)=\sin x
f
(
x
)
=
sin
x
and let
L
L
L
be a positive multiple of
π
\pi
π
. Determine the least positive value of
L
L
L
such that the average value of
f
f
f
on
[
0
,
L
]
[0,L]
[
0
,
L
]
equals
2
π
.
\dfrac{2}{\pi}\,.
π
2
.
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