Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions. : 8xy”, Q(x, y) = −8yx2 (a) P(x, y) л = л ƏD ƏQ ӘР Әх ду л (b) P(x, y) = x + y, Q(x, y) = 7y [ P dx + Q dy = JaD ƏQ ӘР ль (ар) ах D ду - дQ Әх P dx + Q dy = (c) P(x, y) = 2xy = Q(x, y) [pd дQ ах ƏD - dx dy = ӘР ду (d) P(x, y) = 4y, Q(x, y) = X P dx + Q dy = dx dy P dx + Q dy = ӘР ду dx dy = dx dy =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions.
(a) P(x, y) = 8xy2,
Q(x, y) = −8yx2
л
да
ӘР
ах ду
P dx + Q dy =
(b) P(x, y) = x + y, Q(x, y) = 7y
Јас
л
/ (x - ap) ax ay =
dy =
ах
ду
JaD
dx dy =
(c) P(x, y) = 2xy = Q(x, y)
әQ
Әх
P dx + Q dy =
P dx + Q dy =
ӘР
ду
dx dy =
(d) P(x, y) = 4y, Q(x, y) = x
P dx + Q dy =
ӘР
-
ль
(р.
Әх
ду
dx dy =
Transcribed Image Text:Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions. (a) P(x, y) = 8xy2, Q(x, y) = −8yx2 л да ӘР ах ду P dx + Q dy = (b) P(x, y) = x + y, Q(x, y) = 7y Јас л / (x - ap) ax ay = dy = ах ду JaD dx dy = (c) P(x, y) = 2xy = Q(x, y) әQ Әх P dx + Q dy = P dx + Q dy = ӘР ду dx dy = (d) P(x, y) = 4y, Q(x, y) = x P dx + Q dy = ӘР - ль (р. Әх ду dx dy =
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