(b) Find the average value of f(r, y) = x²y? over the region D: 1 //, f(z,4) dA. Area of D (The bar over the f is used to denote average value.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(5) Let D = {(r, y) E R? | |x| + |y| < 1}. The region D is a square diamond (O) in the
ry-plane with corners at the points
(1,0), (0, 1), (-1,0), (0, –1).
Transcribed Image Text:(5) Let D = {(r, y) E R? | |x| + |y| < 1}. The region D is a square diamond (O) in the ry-plane with corners at the points (1,0), (0, 1), (-1,0), (0, –1).
(b) Find the average value of f(x, y) = x²y? over the region D:
1
; //, f(x,y) dA.
Area of D
(The bar over the f is used to denote average value.)
Transcribed Image Text:(b) Find the average value of f(x, y) = x²y? over the region D: 1 ; //, f(x,y) dA. Area of D (The bar over the f is used to denote average value.)
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