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Mathematics
Problem
Which of the following expressions gives the average value of a continuous function
f
f
f
on the interval
[
a
,
b
]
[a,b]
[
a
,
b
]
with
a
<
b
a<b
a
<
b
? a)
1
b
+
a
∫
a
b
f
(
x
)
d
x
\displaystyle \frac{1}{b+a}\int_a^b f(x)\,dx
b
+
a
1
∫
a
b
f
(
x
)
d
x
b)
∫
a
b
f
(
x
)
d
x
\displaystyle \int_a^b f(x)\,dx
∫
a
b
f
(
x
)
d
x
c)
1
b
−
a
∫
a
b
f
(
x
)
d
x
\displaystyle \frac{1}{b-a}\int_a^b f(x)\,dx
b
−
a
1
∫
a
b
f
(
x
)
d
x
d)
1
b
−
a
∫
0
b
f
(
x
)
d
x
\displaystyle \frac{1}{b-a}\int_0^b f(x)\,dx
b
−
a
1
∫
0
b
f
(
x
)
d
x
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