Definition.
Let
f
be a function which is continuous on the closed interval
[a, b]
. The
average value
of
f
from
x = a
to
x = b
is the integral
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Average value and the rate of change.
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Geometrical interpretation of average value.
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Mean Value Theorem for Integrals.
Let
y = f(x)
be a function which is continuous on the closed interval
[a, b]
. Then there exists
c
in the closed interval
[a, b]
such that
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An example.
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An application.
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