WOLFRAM|DEMONSTRATIONS PROJECT

Two Integral Mean Value Theorems

​
a
-3
b
3
striped area = blue area
blue area = striped area
If
f
is continuous on the closed interval
[a,b]
, then there exist
c
1
and
c
2
in
(a,b)
such that
(b-
c
1
)f(
c
1
)=
c
1
∫
a
f(x)dx
and
(
c
2
-a)f(
c
2
)=
b
∫
c
2
f(x)dx
.