$\text { Find the average value of the function } f ( x ) = 48 - 12 x ^ { 2 } \text { over the interval } - 5 \leq s \leq 5 \text {. }$
A) $- 152$
B) $- 52$
C) 148
D) 248
E) $- 252$

Question

$\text { Find the average value of the function } f ( x ) = 48 - 12 x ^ { 2 } \text { over the interval } - 5 \leq s \leq 5 \text {. }$ 
A) $- 152$
B) $- 52$
C) 148
D) 248
E) $- 252$

Quizplus · Accepted Answer

The average value of a function $ f(x) $ over an interval $[a, b]$ is given by $\frac{1}{b-a} \int_{a}^{b} f(x) \, dx$. Here, $ f(x) = 48 - 12x^2 $ and the interval is $[-5, 5]$. Calculate the integral $\int_{-5}^{5} (48 - 12x^2) \, dx$, which results in 0 due to symmetry, and then divide by the interval length $10$, giving an average value of $-52$.