Average Value of a Function

position of sample point in interval

left-hand

right-hand

midpoint

number of intervals

2

Intervals	Approximate Average	Actual Average
1	2.	1.63662
2	1.85355	1.63662

The interval beneath the curve is divided into two or more partitions, and a sample

x

-value is taken from each partition. The user chooses the number of partitions and the position of the sample point. The corresponding values of the function are averaged, and the result is compared with the actual average.

Details

The width of each partition is computed with

b-a

n

.

The position of a sample point in the partition is controlled by the value of the offset (

-0

,

1

, or

1/2

) times the partition width.

The approximate average is computed with

y

1

+

y

2

+

y

3

+...+

y

n

.

The actual average is computed by integration with

1

b-a

b

∫

a

f(x)dx

.

External Links

Riemann Sum (Wolfram MathWorld)

Permanent Citation

Michael Largey, Samuel Leung

"Average Value of a Function"
http://demonstrations.wolfram.com/AverageValueOfAFunction/
Wolfram Demonstrations Project
Published: March 7, 2011