[15] (1) GIVEN: a 0, a constant. Consider the field F: R² → R², F = (2x² + 2y², y + y²) and consider the path, c, once around the triangular region, Q. A (0,0) (a,0), (a,a) in the counter - clock - wise direction. EVALUATE: The circulation integral: HINT: Use Green's theorem. ΘΩ = Δ ABC, {B |C = = = F.ds A S B F = (2x² + 2y², y + y²) X
[15] (1) GIVEN: a 0, a constant. Consider the field F: R² → R², F = (2x² + 2y², y + y²) and consider the path, c, once around the triangular region, Q. A (0,0) (a,0), (a,a) in the counter - clock - wise direction. EVALUATE: The circulation integral: HINT: Use Green's theorem. ΘΩ = Δ ABC, {B |C = = = F.ds A S B F = (2x² + 2y², y + y²) X
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
for the first image attach please do the calculations similar to the second image attach
please please answer everything correctly I would really appreciate if you would answer
this is not a graded question
![[15] (1) GIVEN: a>0, a constant.
Consider the field F: R²
R²,
(xy² - 2y², x²y + y²)
and consider the path, c, once around the triangular region, Q
A = (0,0)
B =
F
=
JΩ = Δ ABC,
(a,0),
(a, a)
in the counter - clockwise direction.
EVALUATE: The circulation integral: F.ds
HINT: Use Green's theorem.
=
√ F·li = [25-35 Jedy
ΖΩ
Qox
Order of integration
must agree with the
functions in the limits,
of integration.
=
b
||
= 4
45
+ √2 + 44, D = {(57) 05752}
y
y
a
2 √² x ² x
2/3
2xy - (2xy - 4y) ady
a
4
+ [ ²ª [ * r & k = ² √ *[ v² [²4
y dy dx
lx
2
3
za
а
=
NOTE: If you chose:
F = (xy²-2y², x²y+x²)
4
Then, F.ds
=
D
(xy² 2y², x²y + y²)
a³
-box must go
from
a function of x, to a higher
function of x.
NOTE: I made a "typo" when I wrote
the given field F a second time. So I gave full
crdit to whichever one you chose.
I also noticed that some of you
are not making your order of integration
consistent with your limits of integration.
Be careful about this.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe343d170-4423-4dcd-9c75-f5f0118e0ff9%2F40d853f8-d97d-4493-96cc-56962cf0eed9%2F97rlqel_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (1) GIVEN: a>0, a constant.
Consider the field F: R²
R²,
(xy² - 2y², x²y + y²)
and consider the path, c, once around the triangular region, Q
A = (0,0)
B =
F
=
JΩ = Δ ABC,
(a,0),
(a, a)
in the counter - clockwise direction.
EVALUATE: The circulation integral: F.ds
HINT: Use Green's theorem.
=
√ F·li = [25-35 Jedy
ΖΩ
Qox
Order of integration
must agree with the
functions in the limits,
of integration.
=
b
||
= 4
45
+ √2 + 44, D = {(57) 05752}
y
y
a
2 √² x ² x
2/3
2xy - (2xy - 4y) ady
a
4
+ [ ²ª [ * r & k = ² √ *[ v² [²4
y dy dx
lx
2
3
za
а
=
NOTE: If you chose:
F = (xy²-2y², x²y+x²)
4
Then, F.ds
=
D
(xy² 2y², x²y + y²)
a³
-box must go
from
a function of x, to a higher
function of x.
NOTE: I made a "typo" when I wrote
the given field F a second time. So I gave full
crdit to whichever one you chose.
I also noticed that some of you
are not making your order of integration
consistent with your limits of integration.
Be careful about this.
![[15] (1)
GIVEN: a>0, a constant.
Consider the field F: R² → R²,
F = (2x² + 2y², y + y²)
and consider the path, c, once around the
triangular region, Q.
A =
B
C = (a,a)
ƏQ
=
Δ ABC,
=
(0,0)
(a,0),
in the counter
clockwise direction.
EVALUATE: The circulation integral: F.ds
So
HINT: Use Green's theorem.
1
1
A
F
D
B
F = (2x² + 2y², y + y²)
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe343d170-4423-4dcd-9c75-f5f0118e0ff9%2F40d853f8-d97d-4493-96cc-56962cf0eed9%2Fikysm7_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (1)
GIVEN: a>0, a constant.
Consider the field F: R² → R²,
F = (2x² + 2y², y + y²)
and consider the path, c, once around the
triangular region, Q.
A =
B
C = (a,a)
ƏQ
=
Δ ABC,
=
(0,0)
(a,0),
in the counter
clockwise direction.
EVALUATE: The circulation integral: F.ds
So
HINT: Use Green's theorem.
1
1
A
F
D
B
F = (2x² + 2y², y + y²)
X
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