QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# QUESTION 2
Find the average value of the function $f(x, y)= 20 - 2 y$ over the rectangle $R=[0,3] \times[0,5]$.
$\bigcirc \mathrm{A} f_{\text {ave }}= 0$
$\bigcirc \mathrm{B} f_{\text {ave }}= 75$
$\bigcirc \mathrm{C} f_{\text {ave }}= 15$
$\bigcirc \mathrm{D} f_{\text {ave }}= 3$
$\bigcirc$ E None of these
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Step 1: Recall the formula for finding the average value of a function over a region.
where $A(R)$ is the area of the region $R$.
Step 2: In this case, the function is $f(x, y) = 20 - 2y$ and the region $R$ is a rectangle with bounds $0 \leq x \leq 3$ and $0 \leq y \leq 5$.
A(R) = (3-0)(5-0) = 15
First, compute the area of the rectangle:
Final Answer
The correct answer is $\bigcirc \mathrm{C}$.
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