Find the exact average value of $f ( x ) = x - 2$ from x = -1 to x = 3.
A) -4
B) -2
C) -1
D) 2

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 $f(x) = x - 2$ from $x = -1$ to $x = 3$, the average value is $\frac{1}{3 - (-1)} \int_{-1}^{3} (x - 2) dx = \frac{1}{4} [(x^2/2 - 2x) |_ {-1}^{3}] = \frac{1}{4} [(9/2 - 6) - (1/2 + 2)] = \frac{1}{4} [(9/2 - 6) - (1/2 + 2)] = \frac{1}{4} [(9/2 - 12/2) - (1/2 + 4/2)] = \frac{1}{4} [-3/2 - 5/2] = \frac{1}{4} \times -8/2 = \frac{1}{4} \times -4 = -1$.

Find the Exact Average Value Of f(x)=x−2f ( x ) = x - 2f(x)=x−2

Find the Exact Average Value Of $f ( x ) = x - 2$