Find the exact average value of $f ( x ) = 9 - x ^ { 2 }$ from x = -3 to x = 3.
A) 0
B) 36
C) 18
D) 6

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 $f(x) = 9 - x^2$ from $x = -3$ to $x = 3$, the average value is $\frac{1}{3 - (-3)} \int_{-3}^{3} (9 - x^2) dx = \frac{1}{6} [9x - \frac{x^3}{3}]_{-3}^{3} = \frac{1}{6} [(27 - 9) - (-27 + 9)] = \frac{1}{6} \cdot 36 = 6$.

Find the Exact Average Value Of f(x)=9−x2f ( x ) = 9 - x ^ { 2 }f(x)=9−x2

Find the Exact Average Value Of $f ( x ) = 9 - x ^ { 2 }$