- ₁₁ f(x, y) dxdy, Calculate the double integrals I = (a) where f(x, y) = 2e²y +3, and D is the domain defined by the relations 0 ≤ x ≤ 2, and 1 ≤ y ≤ 3; (b) where f(x, y) = x²x³ +2, and D is the domain enclosed by the graph of y = x³ and y = 4x with x > 0; (c) where f(x, y) = x²(y-2), and D is the triangle with vertexes (0, 0), (1, 1), (1, 2); (d) where f(x, y) = cos(2x + 3y), and D is the triangle enclosed by the lines x = 0, y = 0, x + y = n; (e) where f(x, y) = 2 + 3(x² + y2)3/2, and D is the unit circle domain centered at (0,0). (Indication: Use polar coordinate system to calculate the integral.)
- ₁₁ f(x, y) dxdy, Calculate the double integrals I = (a) where f(x, y) = 2e²y +3, and D is the domain defined by the relations 0 ≤ x ≤ 2, and 1 ≤ y ≤ 3; (b) where f(x, y) = x²x³ +2, and D is the domain enclosed by the graph of y = x³ and y = 4x with x > 0; (c) where f(x, y) = x²(y-2), and D is the triangle with vertexes (0, 0), (1, 1), (1, 2); (d) where f(x, y) = cos(2x + 3y), and D is the triangle enclosed by the lines x = 0, y = 0, x + y = n; (e) where f(x, y) = 2 + 3(x² + y2)3/2, and D is the unit circle domain centered at (0,0). (Indication: Use polar coordinate system to calculate the integral.)
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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Dd.4.
Transcribed Image Text:Calculate the double integrals I = ff f(x, y)dady,
(a) where f(x, y) = 2e²xy + 3, and D is the domain defined by the relations 0 ≤ x ≤ 2, and 1 ≤ y ≤ 3;
(b) where f(x, y) = x²x³ + 2, and D is the domain enclosed by the graph of y = x³ and y = 4x with x ≥ 0;
(c) where f(x, y) = x²(y − 2), and D is the triangle with vertexes (0,0), (1,1), (1, 2);
(d) where f(x, y) = cos(2x + 3y), and D is the triangle enclosed by the lines x = 0, y = 0, x + y = π;
(e) where f(x,y) 2+3(x² + y²)³/2, and D is the unit circle domain centered at (0,0). (Indication: Use polar
coordinate system to calculate the integral.)
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