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Mathematics
Mathematics
Problem
State which of the following expressions equals the average value of a continuous function
f
f
f
on the closed interval
[
a
,
b
]
[a,b]
[
a
,
b
]
(
a
<
b
a<b
a
<
b
). a)
∫
a
b
f
(
x
)
d
x
\displaystyle\int_a^b f(x)\,dx
∫
a
b
f
(
x
)
d
x
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)
1
b
−
a
∫
0
b
f
(
x
)
d
x
\dfrac{1}{b-a}\displaystyle\int_0^{b} f(x)\,dx
b
−
a
1
∫
0
b
f
(
x
)
d
x
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