The average value of a function
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
on the interval
[
c
,
b
]
\displaystyle {\left[{c},{b}\right]}
[
c
,
b
]
is:
1
b
−
a
∫
a
b
f
(
x
)
d
x
\displaystyle {\frac{{{1}}}{{{b}-{a}}}}\ {\int_{{a}}^{{b}}}{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}
b
−
a
1
∫
a
b
f
(
x
)
d
x
1
c
−
b
∫
c
b
f
(
x
)
d
x
\displaystyle {\frac{{{1}}}{{{c}-{b}}}}\ {\int_{{c}}^{{b}}}{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}
c
−
b
1
∫
c
b
f
(
x
)
d
x
1
c
−
b
∫
b
c
f
(
x
)
d
x
\displaystyle {\frac{{{1}}}{{{c}-{b}}}}\ {\int_{{b}}^{{c}}}{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}
c
−
b
1
∫
b
c
f
(
x
)
d
x
1
b
−
c
∫
c
b
f
(
x
)
d
x
\displaystyle {\frac{{{1}}}{{{b}-{c}}}}\ {\int_{{c}}^{{b}}}{f{{\left({x}\right)}}}\ {\left.{d}{x}\right.}
b
−
c
1
∫
c
b
f
(
x
)
d
x
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