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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 %3и + 6у Step 1 For the transformation x = 6u + v, y = u + 6v, the Jacobian is дх дх 6. д(х, у) a(u, v) du ду = 35 35 ду ду du dv Also, х - Зу 3D (6и + v) — 3(u + 6v) — 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 = 1/6 1/6 x, and this is the image of v = 0 Step 3 The line through (6, 1) and (1, 6) is y = -x+ 9| and this is the image of —и + 1 The line through (0, 0) and (1, 6) is y = 6x and this is the image of u = 0. Submit Skip (you cannot come back)

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 %3и + 6у Step 1 For the transformation x = 6u + v, y = u + 6v, the Jacobian is дх дх 6. д(х, у) a(u, v) du ду = 35 35 ду ду du dv Also, х - Зу 3D (6и + v) — 3(u + 6v) — 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 = 1/6 1/6 x, and this is the image of v = 0 Step 3 The line through (6, 1) and (1, 6) is y = -x+ 9| and this is the image of —и + 1 The line through (0, 0) and (1, 6) is y = 6x and this is the image of u = 0. Submit Skip (you cannot come back)

Elementary Linear Algebra (MindTap Course List)
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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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 %3и + 6у Step 1 For the transformation x = 6u + v, y = u + 6v, the Jacobian is дх дх 6. д(х, у) a(u, v) du ду = 35 35 ду ду du dv Also, х - Зу 3D (6и + v) — 3(u + 6v) — 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 = 1/6 1/6 x, and this is the image of v = 0 Step 3 The line through (6, 1) and (1, 6) is y = -x+ 9| and this is the image of —и + 1 The line through (0, 0) and (1, 6) is y = 6x and this is the image of u = 0. Submit Skip (you cannot come back)
Transcribed Image Text: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 %3и + 6у Step 1 For the transformation x = 6u + v, y = u + 6v, the Jacobian is дх дх 6. д(х, у) a(u, v) du ду = 35 35 ду ду du dv Also, х - Зу 3D (6и + v) — 3(u + 6v) — 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 = 1/6 1/6 x, and this is the image of v = 0 Step 3 The line through (6, 1) and (1, 6) is y = -x+ 9| and this is the image of —и + 1 The line through (0, 0) and (1, 6) is y = 6x and this is the image of u = 0. Submit Skip (you cannot come back)
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