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5. f(x, y) = 8- y; R is the region enclosed by the circles with polar equations r= cos 0 and r= 3 cos 0. %3D 6. f(x, y) = 4; R is the region enclosed by the petal of the rose curve r= sin(20) in the first quadrant. %3D %3D 7. f(x, y) = In (x +y'); R is the annulus enclosed by the cir- cles x + y = 1 and x + y = 4. %3D %3D

5. f(x, y) = 8- y; R is the region enclosed by the circles with polar equations r= cos 0 and r= 3 cos 0. %3D 6. f(x, y) = 4; R is the region enclosed by the petal of the rose curve r= sin(20) in the first quadrant. %3D %3D 7. f(x, y) = In (x +y'); R is the annulus enclosed by the cir- cles x + y = 1 and x + y = 4. %3D %3D

Advanced Engineering Mathematics
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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In Exercises 3- 10, a function f(x, y) is given and a region R of the x-y plane is described. Set up and evaluate ,f(x, y) dA using polar coordinates. 3. f(x, y) = 3x - y+4; R is the region enclosed by the circle x + y? = 1. 4. f(x, y) = 4x + 4y; R is the region enclosed by the circle x? +y = 4. 5. f(x, y) = 8 – y; R is the region enclosed by the circles with polar equations r = cos 0 and r 3 cos 0. 6. f(x, y) = 4; R is the region enclosed by the petal of the rose = sin(20) in the first quadrant. curve r = 7. f(x, y) = In (x² +y?); R is the annulus enclosed by the cir- cles x? +y = 1 and x + y = 4. 8. f(x, y) = 1-x² – y; R is the region enclosed by the circle x* +y = 1. by the
Transcribed Image Text:In Exercises 3- 10, a function f(x, y) is given and a region R of the x-y plane is described. Set up and evaluate ,f(x, y) dA using polar coordinates. 3. f(x, y) = 3x - y+4; R is the region enclosed by the circle x + y? = 1. 4. f(x, y) = 4x + 4y; R is the region enclosed by the circle x? +y = 4. 5. f(x, y) = 8 – y; R is the region enclosed by the circles with polar equations r = cos 0 and r 3 cos 0. 6. f(x, y) = 4; R is the region enclosed by the petal of the rose = sin(20) in the first quadrant. curve r = 7. f(x, y) = In (x² +y?); R is the annulus enclosed by the cir- cles x? +y = 1 and x + y = 4. 8. f(x, y) = 1-x² – y; R is the region enclosed by the circle x* +y = 1. by the
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