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Mathematics
Problem
Which expression gives the average value of a continuous function
f
f
f
on the closed interval
[
a
,
b
]
[a,b]
[
a
,
b
]
(with
a
<
b
a<b
a
<
b
)? a)
f
(
a
+
b
2
)
f\!\left(\dfrac{a+b}{2}\right)
f
(
2
a
+
b
)
b)
1
b
−
a
∫
a
b
f
(
x
)
d
x
\dfrac{1}{b-a}\displaystyle\int_{a}^{b} f(x)\,dx
b
−
a
1
∫
a
b
f
(
x
)
d
x
c)
1
b
∫
a
b
f
(
x
)
d
x
\dfrac{1}{b}\displaystyle\int_{a}^{b} f(x)\,dx
b
1
∫
a
b
f
(
x
)
d
x
d)
f
(
a
)
+
f
(
b
)
2
\dfrac{f(a)+f(b)}{2}
2
f
(
a
)
+
f
(
b
)
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