Two Integral Mean Value Theorems of Flett Type
Two Integral Mean Value Theorems of Flett Type
If is continuous on the closed interval and , then there exist and in such that
f
[a,b]
f(a)=f(b)=α
c
d
(a,b)
(c-a)f(c)=f(x)dx
c
∫
a
(b-d)f(d)=f(x)dx.
b
∫
d
The theorem is illustrated by the equivalence of the blue and striped areas.