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Rewrite the following integral in terms of the variables u = z, v = Vỹ, and w = 2z – y. In particular, find the Jacobian for the change of variables and the new limits of integration: III" f(7,y, 2) dz dy dz = | L| 5(u, v, w)2v dw dv du We used: 1. 1<1<2 translates into 1< u< 2, 2. 0

Rewrite the following integral in terms of the variables u = z, v = Vỹ, and w = 2z – y. In particular, find the Jacobian for the change of variables and the new limits of integration: III" f(7,y, 2) dz dy dz = | L| 5(u, v, w)2v dw dv du We used: 1. 1<1<2 translates into 1< u< 2, 2. 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Rewrite the following integral in terms of the variables u = z, v = Vỹ, and w = 2z – y. In particular, find the Jacobian for the change of variables and the new limits of integration: III" f(7,y, 2) dz dy dz = | L| 5(u, v, w)2v dw dv du We used: 1. 1<1<2 translates into 1< u< 2, 2. 0<ysI² becomes 0< v² < u² or 0 <usu 3. y <z<1+y translates into y <w+ y <1+y or 0 < w < 1. 4. The Jacobian, the determinant of the matrix of the partial derivatives of the variables z, y, and z with respect to the new variables u, v, w is J = 2v.
Transcribed Image Text:Rewrite the following integral in terms of the variables u = z, v = Vỹ, and w = 2z – y. In particular, find the Jacobian for the change of variables and the new limits of integration: III" f(7,y, 2) dz dy dz = | L| 5(u, v, w)2v dw dv du We used: 1. 1<1<2 translates into 1< u< 2, 2. 0<ysI² becomes 0< v² < u² or 0 <usu 3. y <z<1+y translates into y <w+ y <1+y or 0 < w < 1. 4. The Jacobian, the determinant of the matrix of the partial derivatives of the variables z, y, and z with respect to the new variables u, v, w is J = 2v.
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