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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
+
1
f(x)=x^{2}+1
f
(
x
)
=
x
2
+
1
on the interval
[
0
,
2
]
[0,2]
[
0
,
2
]
. If
c
∈
(
0
,
2
)
c\in(0,2)
c
∈
(
0
,
2
)
satisfies
∫
0
2
f
(
x
)
d
x
=
f
(
c
)
(
2
−
0
)
\displaystyle \int_{0}^{2} f(x)\,dx = f(c)(2-0)
∫
0
2
f
(
x
)
d
x
=
f
(
c
)
(
2
−
0
)
, then
c
c
c
equals a)
11
3
\sqrt{\dfrac{11}{3}}
3
11
b)
7
3
\sqrt{\dfrac{7}{3}}
3
7
c)
2
3
\dfrac{2}{\sqrt{3}}
3
2
d)
3
2
\dfrac{\sqrt{3}}{2}
2
3
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