Find the average value of the function over the given interval.
-f(x) = 6 - x on [0, 6]
A) 18
B) 3
C) 6
D) 108

Question

Quizplus · Accepted Answer

The average value of a function $f(x)$ over the interval $[a, b]$ is given by $\frac{1}{b-a} \int_{a}^{b} f(x) dx$. For $f(x) = 6 - x$ on $[0, 6]$, the average value is $\frac{1}{6-0} \int_{0}^{6} (6 - x) dx = \frac{1}{6} [(6x - \frac{1}{2}x^2)]_0^6 = \frac{1}{6} [36 - 18] = 3$.

Find the Average Value of the Function Over the Given