Find the average value of the function over the given interval.
-f(x) = x on [-2, 2]
A) $\frac { 1 } { 2 }$
B) 4
C) 2
D) 1

Question

Find the average value of the function over the given interval.
-f(x) = x on [-2, 2] 
A) $\frac { 1 } { 2 }$
B) 4
C) 2
D) 1

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 $f(x) = x$ on $[-2, 2]$, the average value is $\frac{1}{2-(-2)} \int_{-2}^{2} x dx = \frac{1}{4} [ \frac{x^2}{2} ]_{-2}^{2} = \frac{1}{4} [2 - (-2)] = \frac{1}{4} \cdot 0 = 0$. However, since "0" is not among the options and there seems to be a misunderstanding in the options provided, the explanation shows how to calculate the average value correctly, which is indeed 0, not matching any of the given choices.

Find the Average Value of the Function Over the Given 12\frac { 1 } { 2 }21​

Find the Average Value of the Function Over the Given $\frac { 1 } { 2 }$