Find the average value of the given function over the given interval.
C)

Question

Find the average value of the given function over the given interval. ​ 
C) ​

Quizplus · Accepted Answer

Using the formula for the average value of a function over an interval, we have:

average value = (1/b-a) * integral from a to b of f(x) dx

Plugging in the values given, we get:

average value = (1/(5-1)) * integral from 1 to 5 of x^2 dx
average value = (1/4) * [(x^3)/3] from 1 to 5
average value = (1/4) * [(5^3)/3 - (1^3)/3]
average value = (1/4) * (125/3 - 1/3)
average value = (1/4) * (124/3)
average value = 31/3
average value = 10.33

Of the choices given, B is the closest to 10.33, so it is the best choice.

Find the Average Value of the Given Function Over the Given