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Rewrite the integral: (x-3y)dA where R is the triangular region with vertices (0,0), (2, 1), (1, 2) in the zy-plane using the transformation z = 2u + v, y = u + 2v. (a) Find the image of R (i) Find the image of the side S', joining the vertices (0,0), (2,1) Σ ΣΤfor Σ Sus (ii) Find the image of the side Sz joining the vertices (0,0), (1,2) I

Rewrite the integral: (x-3y)dA where R is the triangular region with vertices (0,0), (2, 1), (1, 2) in the zy-plane using the transformation z = 2u + v, y = u + 2v. (a) Find the image of R (i) Find the image of the side S', joining the vertices (0,0), (2,1) Σ ΣΤfor Σ Sus (ii) Find the image of the side Sz joining the vertices (0,0), (1,2) I

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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Rewrite the integral: (-3y)dA where R is the triangular region with vertices (0, 0), (2, 1), (1, 2) in the zy-plane using the transformation x = 2u + v, y = u + 2v. g (a) Find the image of R (i) Find the image of the side S, joining the vertices (0,0), (2,1) Σ for Σ <us (ii) Find the image of the side Sy joining the vertices (0,0), (1,2): 16 Σ. for Σ <US (iii) Find the Image of the side Sis Joining the vertices (2,1), (1,2) — Σ. Σ for Σ <us (b) Find the Jacobian of the transformation (with alphabetical ordering) Σ Σ (c) Write the transformed Integral: where a = b= e= d= Σ (d) Evaluate the integral: + Σ Σand Σ Σ Σ J Ja Σ Σ dudu, Σ Σ Σ Σ
Transcribed Image Text:Rewrite the integral: (-3y)dA where R is the triangular region with vertices (0, 0), (2, 1), (1, 2) in the zy-plane using the transformation x = 2u + v, y = u + 2v. g (a) Find the image of R (i) Find the image of the side S, joining the vertices (0,0), (2,1) Σ for Σ <us (ii) Find the image of the side Sy joining the vertices (0,0), (1,2): 16 Σ. for Σ <US (iii) Find the Image of the side Sis Joining the vertices (2,1), (1,2) — Σ. Σ for Σ <us (b) Find the Jacobian of the transformation (with alphabetical ordering) Σ Σ (c) Write the transformed Integral: where a = b= e= d= Σ (d) Evaluate the integral: + Σ Σand Σ Σ Σ J Ja Σ Σ dudu, Σ Σ Σ Σ
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