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Mathematics
Problem
For a continuous function
f
f
f
defined on
[
a
,
b
]
[a,b]
[
a
,
b
]
, which of the following expressions gives the average value of
f
f
f
over the interval? a)
f
(
a
)
+
f
(
b
)
2
\dfrac{f(a)+f(b)}{2}
2
f
(
a
)
+
f
(
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
∫
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
d)
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
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