Find the average value of the function over the given interval.
-f(x) = 10 - x on [0, 10]
A) 500
B) 5
C) 50
D) 10

Question

Quizplus · Accepted Answer

The average value of a function $f(x)$ over an interval $[a, b]$ is given by $\frac{1}{b-a} \int_{a}^{b} f(x) dx$. For $f(x) = 10 - x$ on $[0, 10]$, the average value is $\frac{1}{10-0} \int_{0}^{10} (10 - x) dx = \frac{1}{10} [(10x - \frac{1}{2}x^2)]_{0}^{10} = \frac{1}{10} [100 - 50] = 5$.

Find the Average Value of the Function Over the Given