Problem 12 (Answer the following three questions) Let T : R² → R² be a transformation given by T : (u, v) → (x, y), where x = u + v and y = v³. The region Rin xy-plane is given by -y ≤x≤1-y, 0≤ y ≤ 2. Let S be the corresponding region in uv-plane given by a ≤ u≤ b, c≤ v≤d. Find a, b, c, d. Ans: 0, 1, 0, 2 Problem 13 Compute the Jacobian of T i.e., det JT. Problem 14 Using the change of variable formula find [[ f(x, y)dA = ſſ f(x(u, v), y(u, v))| det JŢ| du dv R SS₁ 1 JR 3y²/3 dA. Ans: 3v² Ans: 2
Problem 12 (Answer the following three questions) Let T : R² → R² be a transformation given by T : (u, v) → (x, y), where x = u + v and y = v³. The region Rin xy-plane is given by -y ≤x≤1-y, 0≤ y ≤ 2. Let S be the corresponding region in uv-plane given by a ≤ u≤ b, c≤ v≤d. Find a, b, c, d. Ans: 0, 1, 0, 2 Problem 13 Compute the Jacobian of T i.e., det JT. Problem 14 Using the change of variable formula find [[ f(x, y)dA = ſſ f(x(u, v), y(u, v))| det JŢ| du dv R SS₁ 1 JR 3y²/3 dA. Ans: 3v² Ans: 2
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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![Problem 12 (Answer the following three questions)
Let T : R² → R² be a transformation given by T : (u, v) → (x, y), where x = u + v and y = v³. The region
R in xy-plane is given by -y ≤x≤1-y, 0≤y ≤ 2. Let S be the corresponding region in uv-plane given
by a ≤ u ≤ b, c ≤ v ≤ d. Find a, b,c, d.
Ans: 0, 1, 0, 2
Problem 13
Compute the Jacobian of T i.e., det JȚ.
Problem 14
Using the change of variable formula
find
ſſ ƒ(x, y)dA = ſ[¸ ƒ(x(u,v), y(u, v))| det Jr] du dv
R
SS₁
1
R 3y²/3
dA.
Ans: 3²
Ans: 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2Fd1ff8b3a-8149-4102-911a-a6fea1fcfae4%2Fz57k7h_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 12 (Answer the following three questions)
Let T : R² → R² be a transformation given by T : (u, v) → (x, y), where x = u + v and y = v³. The region
R in xy-plane is given by -y ≤x≤1-y, 0≤y ≤ 2. Let S be the corresponding region in uv-plane given
by a ≤ u ≤ b, c ≤ v ≤ d. Find a, b,c, d.
Ans: 0, 1, 0, 2
Problem 13
Compute the Jacobian of T i.e., det JȚ.
Problem 14
Using the change of variable formula
find
ſſ ƒ(x, y)dA = ſ[¸ ƒ(x(u,v), y(u, v))| det Jr] du dv
R
SS₁
1
R 3y²/3
dA.
Ans: 3²
Ans: 2
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