Trapezoidal Rule to find the average value of f(x)

From http://www.intmath.com/integration/5-trapezoidal-rule.php

Area≈​2​​1​​(y​0​​+y​1​​)Δx+​2​​1​​(y​1​​+y​2​​)Δx+​2​​1​​(y​2​​+y​3​​)Δx+

Area≈Δx(​2​​y​0​​​​+y​1​​+y​2​​+y​3​​+…+​2​​y​n​​​​) for uniform grid


The trapezoidal rule finds the area. To get the average 
value, you will need to divide the area by b-a which is the
 the difference between the final and initial x values.