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Change of Variable using Jacobians Evaluate the integrals by making the indicated change of variables. 1. f (3x - 4y) dxdy boundary of R: y = 3x, y = x, x = 4 change of variables: x = u-2v, y = 3u - v

Change of Variable using Jacobians Evaluate the integrals by making the indicated change of variables. 1. f (3x - 4y) dxdy boundary of R: y = 3x, y = x, x = 4 change of variables: x = u-2v, y = 3u - v

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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Change of Variable using Jacobians Evaluate the integrals by making the indicated change of variables. 1. (3x - 4y)dxdy boundary of R: y = 3x, y = x, x = 4 change of variables: x = u-2v, y = 3u - v 2. S (x - y)² cos² (x + y)dxdy boundary of R: the square with vertices (0, 1), (1, 2), (2, 1), (1, 0) change of variables: u = x - y, v = x + y 3. R sindxdy boundary of R: the trapezoid with vertices (1, 1), (2, 2), (4, 0), (2, 0) change of variables: u = y - x, v = y + x 4. SSR y-2x boundary of R: the trapezoid with vertices (-1, 0), (-2, 0), (0, 4), (0, 2) change of variables: u = y - 2x, v = 2y + x 2y+x dxdy
Transcribed Image Text:Change of Variable using Jacobians Evaluate the integrals by making the indicated change of variables. 1. (3x - 4y)dxdy boundary of R: y = 3x, y = x, x = 4 change of variables: x = u-2v, y = 3u - v 2. S (x - y)² cos² (x + y)dxdy boundary of R: the square with vertices (0, 1), (1, 2), (2, 1), (1, 0) change of variables: u = x - y, v = x + y 3. R sindxdy boundary of R: the trapezoid with vertices (1, 1), (2, 2), (4, 0), (2, 0) change of variables: u = y - x, v = y + x 4. SSR y-2x boundary of R: the trapezoid with vertices (-1, 0), (-2, 0), (0, 4), (0, 2) change of variables: u = y - 2x, v = 2y + x 2y+x dxdy
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