3. Evaluate the double integrals. -1/2 (a) [fx(1+ y²) d4; R is the region in the first quadrant enclosed by y=x², y = 4, and x = 0. (b) ff xy d4; R is the region enclosed by y=√x, y=6–x, and y=0. R (c) ff (x-1) d4; R is the region in the first quadrant enclosed between y=x and y=x³. R

Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Conic Sections
Section8.2: More Parabolas And Some Circles
Problem 63.5PS
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3. Evaluate the double integrals.
-1/2
(a) ſfx(1+y²)¹¹² dA; R is the region in the first quadrant enclosed by y=x², y = 4, and x = 0.
(b) ſſ xy d4; R is the region enclosed by y=√x, y=6–x, and y=0.
(c) ff (x
(x-1) dA; R is the region in the first quadrant enclosed between y = x and y=x².
(d) ff sin dA, where R is the region bounded by y=√x, y = 2, and x = 0. [Hint: Choose
the order of integration carefully]
Transcribed Image Text:3. Evaluate the double integrals. -1/2 (a) ſfx(1+y²)¹¹² dA; R is the region in the first quadrant enclosed by y=x², y = 4, and x = 0. (b) ſſ xy d4; R is the region enclosed by y=√x, y=6–x, and y=0. (c) ff (x (x-1) dA; R is the region in the first quadrant enclosed between y = x and y=x². (d) ff sin dA, where R is the region bounded by y=√x, y = 2, and x = 0. [Hint: Choose the order of integration carefully]
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