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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) = xy², Q(x, y) = -yx² Topd P dx + Q dy = aQ /[(25) dx dy - [ = ?х ду (b) P(x, y) = x + y, Q(x, y) = 4y Jooº P dx + Q dy = aQ ap // ( 12² - 2+ ) ax ay = [ dx dy əx ду (c) P(x, y) = 8xy = Q(x, y) [Pdx P dx + Q dy = ƏQ 16 (00-) dx dy-1 = ду 00

Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions. (a) P(x, y) = xy², Q(x, y) = -yx² Topd P dx + Q dy = aQ /[(25) dx dy - [ = ?х ду (b) P(x, y) = x + y, Q(x, y) = 4y Jooº P dx + Q dy = aQ ap // ( 12² - 2+ ) ax ay = [ dx dy əx ду (c) P(x, y) = 8xy = Q(x, y) [Pdx P dx + Q dy = ƏQ 16 (00-) dx dy-1 = ду 00

Advanced Engineering Mathematics
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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Verify Green's theorem for the disc D with center (0, 0) and radius R and the following functions. (a) P(x, y) = xy², Q(x, y) = -yx² №ooº P dx + Q dy = = aQ 16 (00-or) dx dy - [ = ?х ду (b) P(x, y) = x + y, Q(x, y) = 4y Joof P dx + Q dy = / 6 (2²-2) ∞xov - 1 (c) P(x, y) = 8xy = Q(x, y) [Pox+Qay- P dx + Q dy = aQ 11 (32²-3²) dx dy - = əx ду 1 (d) P(x, y) = 4y, Q(x, y) = x P dx + Q dy= = lac aQ // ( 08²2-3²) dx dy = [ əx ду 7
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) = xy², Q(x, y) = -yx² №ooº P dx + Q dy = = aQ 16 (00-or) dx dy - [ = ?х ду (b) P(x, y) = x + y, Q(x, y) = 4y Joof P dx + Q dy = / 6 (2²-2) ∞xov - 1 (c) P(x, y) = 8xy = Q(x, y) [Pox+Qay- P dx + Q dy = aQ 11 (32²-3²) dx dy - = əx ду 1 (d) P(x, y) = 4y, Q(x, y) = x P dx + Q dy= = lac aQ // ( 08²2-3²) dx dy = [ əx ду 7
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