The average value favg of the functionƒ : R² → R over the domain D is given by the formula favg 1 D // f(x, y) dA, where m(D) is the measure of the size of %3D D (in general, this could be length, area, volume, etc.) Find the average value of the function f(x, y) = x sin?(xy) on the square [0, 7] × [0, r].
The average value favg of the functionƒ : R² → R over the domain D is given by the formula favg 1 D // f(x, y) dA, where m(D) is the measure of the size of %3D D (in general, this could be length, area, volume, etc.) Find the average value of the function f(x, y) = x sin?(xy) on the square [0, 7] × [0, r].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The *average value* \( f_{\text{avg}} \) of the function \( f : \mathbb{R}^2 \rightarrow \mathbb{R} \) over the domain \( D \) is given by the formula
\[
f_{\text{avg}} = \frac{1}{m(D)} \iint_D f(x,y) \, dA,
\]
where \( m(D) \) is the measure of the size of \( D \) (in general, this could be length, area, volume, etc.)
Find the average value of the function \( f(x, y) = x \sin^2(xy) \) on the square \([0, \pi] \times [0, \pi]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fd531f0-250f-490d-993a-3449a32c15bc%2F898ddfcf-035b-4d84-86ec-5a9ba6404e44%2Fal93xkp_processed.png&w=3840&q=75)
Transcribed Image Text:The *average value* \( f_{\text{avg}} \) of the function \( f : \mathbb{R}^2 \rightarrow \mathbb{R} \) over the domain \( D \) is given by the formula
\[
f_{\text{avg}} = \frac{1}{m(D)} \iint_D f(x,y) \, dA,
\]
where \( m(D) \) is the measure of the size of \( D \) (in general, this could be length, area, volume, etc.)
Find the average value of the function \( f(x, y) = x \sin^2(xy) \) on the square \([0, \pi] \times [0, \pi]\).
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