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Average value Compute the average value of the following
Chapter 11, Problem 24E(choose chapter or problem)
Average value Compute the average value of the following functions over the region R.
f(x, y)=4-x-y ; \(R=\{(x, y): 0 \leq x \leq 2,0 \leq y \leq 2\}\)
Questions & Answers
QUESTION:
Average value Compute the average value of the following functions over the region R.
f(x, y)=4-x-y ; \(R=\{(x, y): 0 \leq x \leq 2,0 \leq y \leq 2\}\)
ANSWER:Solution 24EStep 1 of 2:In this problem we need to compute the average value of the function Definition : The average value or mean value of an integrable function f( x, y) over the set D is the number Given : f( x, y) = 4 -x -y and Hence , the Area of D = (2)(2) = 4.Consider , Let us consider , I = = Evaluate the inner integral with respect to x.That is , = Take the constants out , we get : = Therefore ,