The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of it. The area of the red is thus, 4-(pi/4). The boundar yof the shape (shown in blue) is composed of 3 segments and an arc of a circle. if we anted to compute the work along the boundary we would have to parameterize all 4 edges and compute separate line integrals for each. This would be a lot of work unless we had a very simple force field and simple parameterizations. But since our figure is in R^2 and the boundary is a simple closed curve, we can apply Geen's theorem. Apply Green's Theorem to compute the work along the boundary of the red shaded region given the force field is: F(x,y) = vector brackets(y, 2x + tan(tan(y))) %3D Assume the boundary is oriented counter-clockwise А.) 0 B.) 2 - (pi/8) С) 1 D.) 4 E.) 4 - (pi/4)
The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of it. The area of the red is thus, 4-(pi/4). The boundar yof the shape (shown in blue) is composed of 3 segments and an arc of a circle. if we anted to compute the work along the boundary we would have to parameterize all 4 edges and compute separate line integrals for each. This would be a lot of work unless we had a very simple force field and simple parameterizations. But since our figure is in R^2 and the boundary is a simple closed curve, we can apply Geen's theorem. Apply Green's Theorem to compute the work along the boundary of the red shaded region given the force field is: F(x,y) = vector brackets(y, 2x + tan(tan(y))) %3D Assume the boundary is oriented counter-clockwise А.) 0 B.) 2 - (pi/8) С) 1 D.) 4 E.) 4 - (pi/4)
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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Transcribed Image Text:The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of it. The area
of the red is thus,
4-(pi/4).
The boundar yof the shape (shown in blue) is composed of 3 segments and an arc of a circle. if we anted to
compute the work along the boundary we would have to parameterize all 4 edges and compute separate
line integrals for each. This would be a lot of work unless we had a very simple force field and simple
parameterizations. But since our figure is in R^2 and the boundary is a simple closed curve, we can apply
Geen's theorem. Apply Green's Theorem to compute the work along the boundary of the red shaded
region given the force field is:
F(x,y) = vector brackets(y, 2x + tan(tan(y)))
Assume the boundary is oriented counter-clockwise
A.) O
B.) 2 - (pi/8)
C.) 1
D.) 4
E.) 4 - (pi/4)
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