WOLFRAM|DEMONSTRATIONS PROJECT

The Integral Mean Value Theorem: An Illustration

​
position
0.8
function
sin(x)

2
x
-4
-x

log(x+1)
2
(3-x)
x-2
cos(x)
x-1
2
x
There exists a point c inside [a, b] such that (b-a)f(c) =
b
∫
a
f(x)x.
There is at least one point in the interval such that the area of the rectangle (yellow) and the area below the curve (blue) are the same. The function value at this point is defined to be the average value of the function over the interval.