(5) Let D = {(x, y) E R? ||r| + |y| < 1}. The region D is a square diamond () in the ry-plane with corners at the points (1,0), (0,1), (-1,0), (0, -1). (a) Let f(r, y) = x²y?. Compute // f(x, y) dA. %3D Exploit symmetry: f(-2, y) = f(x, -y) = f(-x,-y) = f(r, y).

(5) Let D = {(x, y) E R? ||r| + |y| < 1}. The region D is a square diamond () in the ry-plane with corners at the points (1,0), (0,1), (-1,0), (0, -1). (a) Let f(r, y) = x²y?. Compute // f(x, y) dA. %3D Exploit symmetry: f(-2, y) = f(x, -y) = f(-x,-y) = f(r, y).

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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Question

{(x, y) € R? | |2| + |y| < 1}. The region D is a square diamond (0) in the
(5) Let D =
ry-plane with corners at the points
(1,0), (0, 1), (-1, 0), (0, –1).
(a) Let f(x, y) = a²y². Compute // f(x, y) dA.
Exploit symmetry:
f(-x, y) = f(x, -y) = f(-x, -y) = f(x, y).

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