Solve Step 2 beyond Use the given transformation to evaluate the given integral, where R is the triangular region with vertices (0,0), (6, 1), and (1, 6).(х — Зу) dA, х 3D би + v, у %3D и + буStep 1For the transformation x = 6u + v, y = u + 6v, the Jacobian is61a(x, y) =dudv35=a(u, v)дудуdvдиAlso,х —— Зу %3D (би + v) — 3(и + би) %3D Зи — 17V.Step 2To find the region S in the uv-plane which corresponds to R, we find the corresponding boundaries. The linethough (0, 0) and (6, 1) is y =X, and this is the image of v =

Given:0,0 6,1 and 1,6∬R x-3y dA , x=6u+v and y=u+6vThe line through 0,0 and 6,1 is y= ? ximage…

Answered: P 2 o find the region S in the uv-plane…

P 2 o find the region S in the uv-plane which corresponds to R, we find the corresponding boundaries. The line hough (0, 0) and (6, 1) is y = X, and this is the image of v =

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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Solve Step 2 beyond

Use the given transformation to evaluate the given integral, where R is the triangular region with vertices (0,
0), (6, 1), and (1, 6).
(х — Зу) dA, х 3D би + v, у %3D и + бу
Step 1
For the transformation x = 6u + v, y = u + 6v, the Jacobian is
6
1
a(x, y) =
du
dv
35
=
a(u, v)
ду
ду
dv
ди
Also,
х —
— Зу %3D (би + v) — 3(и + би) %3D Зи — 17
V.
Step 2
To find the region S in the uv-plane which corresponds to R, we find the corresponding boundaries. The line
though (0, 0) and (6, 1) is y =
X, and this is the image of v =

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