RHS: Qué (3.) Verify Green's Theorem for the field F = (x²y, x) over the closed region given below with clockwise orientation, = 1 § Fidλ = - SS (Qx-Py) dA D Py = x² 11-x2 1-x² -SS (1-x²) dydx 1 (1-x²)2dx LHS : GO SREE SPAR + C, : *(+) = -15+41 F(A) - y = 1-x² 0.5 -0.5 = ~ even Symm 11 = = 11 = = -2 (1-2x²+x")dx -2 ₤1 [+] -2 [15-10-7) 2 B 16 15 15 [%] ⇒ = F' <1, -2t> F-F'= t²-t-2t² = -4 -t² SE₁dri = -S(t" + t³) dt CI = -1 -25/24+00 by Symmetry 4 2 -[#] V -2 = (ઙે +3) -2 (4) = -16 C₂i F = <-t, o> -15821 F = <-1, 0> F(F) = <0, -+> ル ༤ F(r)•F' F (F) • F' => SF JG = 0 -16 +0 = 16 15
RHS: Qué (3.) Verify Green's Theorem for the field F = (x²y, x) over the closed region given below with clockwise orientation, = 1 § Fidλ = - SS (Qx-Py) dA D Py = x² 11-x2 1-x² -SS (1-x²) dydx 1 (1-x²)2dx LHS : GO SREE SPAR + C, : *(+) = -15+41 F(A) - y = 1-x² 0.5 -0.5 = ~ even Symm 11 = = 11 = = -2 (1-2x²+x")dx -2 ₤1 [+] -2 [15-10-7) 2 B 16 15 15 [%] ⇒ = F' <1, -2t> F-F'= t²-t-2t² = -4 -t² SE₁dri = -S(t" + t³) dt CI = -1 -25/24+00 by Symmetry 4 2 -[#] V -2 = (ઙે +3) -2 (4) = -16 C₂i F = <-t, o> -15821 F = <-1, 0> F(F) = <0, -+> ル ༤ F(r)•F' F (F) • F' => SF JG = 0 -16 +0 = 16 15
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please review and solve the following problem. The screenshot listed already has some work done and the correct answer listed. Please solve the problem and include an explanation of how the work was solved. Also, Please make sure to double check the answer provided matches up with the screenshot and the work is properly formatted so I am able to follow along. Thanks :)
![RHS:
Qué
(3.)
Verify Green's Theorem for the field F
=
(x²y, x) over the closed region given below with
clockwise orientation,
= 1
§ Fidλ = - SS (Qx-Py) dA
D
Py = x²
11-x2
1-x²
-SS (1-x²) dydx
1
(1-x²)2dx
LHS :
GO SREE SPAR
+
C, :
*(+) = <t, 1-+²>
-15+41
F(A) - <t²(1-{²), =>
y = 1-x²
0.5
-0.5
=
~
even
Symm
11
=
=
11
=
=
-2 (1-2x²+x")dx
-2
₤1
[+]
-2 [15-10-7)
2
B
16
15
15
[%]
⇒
=
F' <1, -2t>
F-F'= t²-t-2t²
= -4 -t²
SE₁dri = -S(t" + t³) dt
CI
=
-1
-25/24+00
by
Symmetry
4
2
-[#]
V -2
=
(ઙે +3)
-2 (4)
= -16
C₂i
F = <-t, o>
-15821
F = <-1, 0>
F(F) = <0, -+>
ル
༤
F(r)•F'
F (F) • F' =>
SF JG = 0
-16
+0 =
16
15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4effdf1a-67d0-42fb-b95c-7c4b54ad0624%2F1117b5c3-602e-440d-bac8-71037f72f73b%2Fwukw65i_processed.png&w=3840&q=75)
Transcribed Image Text:RHS:
Qué
(3.)
Verify Green's Theorem for the field F
=
(x²y, x) over the closed region given below with
clockwise orientation,
= 1
§ Fidλ = - SS (Qx-Py) dA
D
Py = x²
11-x2
1-x²
-SS (1-x²) dydx
1
(1-x²)2dx
LHS :
GO SREE SPAR
+
C, :
*(+) = <t, 1-+²>
-15+41
F(A) - <t²(1-{²), =>
y = 1-x²
0.5
-0.5
=
~
even
Symm
11
=
=
11
=
=
-2 (1-2x²+x")dx
-2
₤1
[+]
-2 [15-10-7)
2
B
16
15
15
[%]
⇒
=
F' <1, -2t>
F-F'= t²-t-2t²
= -4 -t²
SE₁dri = -S(t" + t³) dt
CI
=
-1
-25/24+00
by
Symmetry
4
2
-[#]
V -2
=
(ઙે +3)
-2 (4)
= -16
C₂i
F = <-t, o>
-15821
F = <-1, 0>
F(F) = <0, -+>
ル
༤
F(r)•F'
F (F) • F' =>
SF JG = 0
-16
+0 =
16
15
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