Find the average value of the function f over the given region.
-f(x, y) = 2x + 8y; R = {(x, y): 0 $\le$x $\le$ 1, 0$\le$ y $\le$ 1}
A) 10
B) 5
C) 6
D) 9

Question

Quizplus · Accepted Answer

The average value of a function $f(x, y)$ over a region $R$ is given by $\frac{1}{A(R)} \int \int_R f(x, y) dA$, where $A(R)$ is the area of the region $R$. For the given function $f(x, y) = 2x + 8y$ over the square region $R$ with $0 \le x \le 1$ and $0 \le y \le 1$, the area $A(R) = 1 \times 1 = 1$. The double integral of $f(x, y)$ over $R$ is $\int_0^1 \int_0^1 (2x + 8y) dx dy$. Computing this gives $5$, thus the average value is $5$.

Find the Average Value of the Function F Over the Given