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Two Integral Mean Value Theorems of Flett Type

​
α
70
blue area = yellow area
blue area = yellow area
Solve
:Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.
Solve
:Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.
If
f
is continuous on the closed interval
[a,b]
and
f(a)=f(b)=α
, then there exist
c
and
d
in
(a,b)
such that
(c-a)f(c)=
c
∫
a
f(x)dx
and
(b-d)f(d)=
b
∫
d
f(x)dx.
The theorem is illustrated by the equivalence of the blue and striped areas.​
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