A) Suppose F(xy)- М(х,у) і + N(x,y) j is a vector field on the xy plane such that F•dr = 0 Se I F•dr = - 6 C2 So F•dr = 5 where the curves C,,C2,C3 are oriented as shown in the figure below. If R denotes the interior of the triangle shown in the figure, then ƏN ƏM' dA = dx B) Consider a second vector field G(x,y)- 2 N(x,y) і - 2 М(х,у) ј where N,M are the same functions used to define F(x,y). Then the outward flux of G across the triangle shown in the figure shown below equals outward flux =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A) Suppose
F(x,y)= M(x,y) i + N(x,y) j
is a vector field on the xy plane such that
|c
F•dr = 0
F•dr = -6
|F•dr = 5
where the curves C,,C2,C3 are oriented as shown in the figure below.
If R denotes the interior of the triangle shown in the figure, then
aN
ƏM
dx
dA =|
dy
R
B) Consider a second vector field
G(x,y)= 2 N(x,y) i - 2 M(x,y) j
where N,M are the same functions used to define F(x,y).
Then the outward flux of G across the triangle shown in the figure shown below equals
outward flux
Transcribed Image Text:A) Suppose F(x,y)= M(x,y) i + N(x,y) j is a vector field on the xy plane such that |c F•dr = 0 F•dr = -6 |F•dr = 5 where the curves C,,C2,C3 are oriented as shown in the figure below. If R denotes the interior of the triangle shown in the figure, then aN ƏM dx dA =| dy R B) Consider a second vector field G(x,y)= 2 N(x,y) i - 2 M(x,y) j where N,M are the same functions used to define F(x,y). Then the outward flux of G across the triangle shown in the figure shown below equals outward flux
C3
C2
R
C1
Transcribed Image Text:C3 C2 R C1
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