Let C denote the boundary of the region R, oriented counterclockwise. Consider the vector fieldF=3' 3a) Use Green's Theorem to write a double integral which computes the circulation (work)of F along the curve C:F•dr =Rdy dxb) In order to do the previous double integral, we want to use the substitutionX= uv',- 1y = uvThe Jacobian of this transformation isJ(u,v)=|The integral you found in part a) becomesu2 v2+ v um ) dv duu1 v1whereu1=u2=v1=v2=n =m=OO DO NO Suppose Ris the region on the xy plane in the first quadrant determined by the inequalities6< xys 10y6s<10RLet C denote the boundary of the region R, oriented counterclockwise. Consider the vector field(-F=3' 3a) Use Green's Theorem to write a double integral which computes the circulation (work)of F along the curve C:S.F•dr =dy dxRb) In order to do the previous double integral, we want to use the substitutionx = uv-1,y= uvThe Jacobian of this transformation isJ(u,v)=

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Suppose R is the region on the xy plane in the first quadrant determined by the inequalities 6sxys 10 6s10 R Let C denote the boundary of the region R, oriented counterclockwise. Consider the vector field (-) F= a) Use Green's Theorem to write a double integral which computes the circulation (work) of F along the curve C: F•dr = R b) In order to do the previous double integral, we want to use the substitution X = uv -1 , y=uv The Jacobian of this transformation is J(u,v)=

Suppose R is the region on the xy plane in the first quadrant determined by the inequalities 6sxys 10 6s10 R Let C denote the boundary of the region R, oriented counterclockwise. Consider the vector field (-) F= a) Use Green's Theorem to write a double integral which computes the circulation (work) of F along the curve C: F•dr = R b) In order to do the previous double integral, we want to use the substitution X = uv -1 , y=uv The Jacobian of this transformation is J(u,v)=

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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Question

Let C denote the boundary of the region R, oriented counterclockwise. Consider the vector field
F=
3' 3
a) Use Green's Theorem to write a double integral which computes the circulation (work)
of F along the curve C:
F•dr =
R
dy dx
b) In order to do the previous double integral, we want to use the substitution
X= uv',
- 1
y = uv
The Jacobian of this transformation is
J(u,v)=|
The integral you found in part a) becomes
u2 v2
+ v um ) dv du
u1 v1
where
u1=
u2=
v1=
v2=
n =
m=
OO DO NO

Suppose Ris the region on the xy plane in the first quadrant determined by the inequalities
6< xys 10
y
6s<10
R
Let C denote the boundary of the region R, oriented counterclockwise. Consider the vector field
(-
F=
3' 3
a) Use Green's Theorem to write a double integral which computes the circulation (work)
of F along the curve C:
S.
F•dr =
dy dx
R
b) In order to do the previous double integral, we want to use the substitution
x = uv-1,
y= uv
The Jacobian of this transformation is
J(u,v)=

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