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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
x
+
x
2
f(x)=\sin x + x^{2}
f
(
x
)
=
sin
x
+
x
2
on
[
0
,
π
]
[0,\pi]
[
0
,
π
]
. How many distinct values of
c
c
c
in
(
0
,
π
)
(0,\pi)
(
0
,
π
)
satisfy
∫
0
π
f
(
x
)
d
x
=
f
(
c
)
π
\displaystyle \int_{0}^{\pi} f(x)\,dx = f(c)\,\pi
∫
0
π
f
(
x
)
d
x
=
f
(
c
)
π
? a) Exactly two b) None c) Exactly one d) More than two
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