6 Let D = {(x, y) € R² : 0 ≤ y ≤ 3,-√√9-y² ≤ x ≤ √√√3-y} and g continuous function. Then the integral fog(x,y) dx dy equals √3 +3 (A) fºs (g(x, y) dy) dr + f(+³9(x, y) dy) da √√3 (B) ſº, (* g(x, y) dy) dx + √³ (5²² g(x, y) dy) dr 2 (©) ſº; (ſo™*¯° 9(x, y) dy) dx + √³ (+3 g(x,y) dy) dr (√ Cz²+3 (D) Sº, (*¹²*¹ g(x, y) dy) dx + ³ (²+³ g(x, y) dy) dr ↑ 3

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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6 Let D = {(x, y) € R² : 0 ≤ y ≤ 3, − √√9 - y² ≤ x ≤ √√3-y} and g: D → R be a
continuous function. Then the integral g(x, y) dx dy equals
√9-7
+3
(A) Sº, (ſovª** g(x, y) dy) dx + ³
So
(2+³ g(x, y) dy) d
9-T2
√3
(B) ſº, (ſo¯¯¯ 9(x, y) dy) dr + ſ№³ (√²-³ g(x, y) dy) da
(C) ſº, (ſ¯¯¯° g(x,y) dy) da + √√³ (ƒ-²²+³ g(x, y) dy) da
(D) Sº, (*¹*¹ g(x, y) dy) dr + f (²+3 g(x, y) dy) a
(%
da (√3²+³
Transcribed Image Text:6 Let D = {(x, y) € R² : 0 ≤ y ≤ 3, − √√9 - y² ≤ x ≤ √√3-y} and g: D → R be a continuous function. Then the integral g(x, y) dx dy equals √9-7 +3 (A) Sº, (ſovª** g(x, y) dy) dx + ³ So (2+³ g(x, y) dy) d 9-T2 √3 (B) ſº, (ſo¯¯¯ 9(x, y) dy) dr + ſ№³ (√²-³ g(x, y) dy) da (C) ſº, (ſ¯¯¯° g(x,y) dy) da + √√³ (ƒ-²²+³ g(x, y) dy) da (D) Sº, (*¹*¹ g(x, y) dy) dr + f (²+3 g(x, y) dy) a (% da (√3²+³
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