Find the average value of the function $f ( x ) = x e ^ { - x / 3 }$ over the interval from 0 to 4.Round to two decimal places.
A)0.87
B)3.46
C)10.86
D)7.79

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 $f(x) = x e^{-x/3}$ over the interval from 0 to 4, we calculate the integral and then divide by the length of the interval, which is 4 - 0 = 4. The integral of $x e^{-x/3}$ can be found using integration by parts or looking it up in a table of integrals. After performing the integration and dividing by 4, the result is approximately 0.87, which matches choice A.

Find the Average Value of the Function f(x)=xe−x/3f ( x ) = x e ^ { - x / 3 }f(x)=xe−x/3

Find the Average Value of the Function $f ( x ) = x e ^ { - x / 3 }$