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Solve the following integral: where the region R is: =ff₁₂₁²- R Consider the change of variables: I = +−(z+s) drdy R = {(x, y) = R² : 0 ≤ y ≤ x, 2 ≤ x + y ≤ 3} u= x + y Y x V= 1. Draw the region R both in the x - y plane and in the u- v plane. 2. Invert the system writing the coordinates and y as function of u and v. 3. Use the change of variables from x - y to u- v to solve the integral I.

Solve the following integral: where the region R is: =ff₁₂₁²- R Consider the change of variables: I = +−(z+s) drdy R = {(x, y) = R² : 0 ≤ y ≤ x, 2 ≤ x + y ≤ 3} u= x + y Y x V= 1. Draw the region R both in the x - y plane and in the u- v plane. 2. Invert the system writing the coordinates and y as function of u and v. 3. Use the change of variables from x - y to u- v to solve the integral I.

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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Solve the following integral: where the region R is: I Consider the change of variables: = 1₁₂ R -(x+y)² R = {(x, y) = R² : 0 ≤ y ≤ x, 2 ≤ x + y ≤3} u = x + y Y x dxdy V = 1. Draw the region R both in the x - y plane and in the u- v plane. 2. Invert the system writing the coordinates and y as function of u and v. 3. Use the change of variables from x - y to u - v to solve the integral I.
Transcribed Image Text:Solve the following integral: where the region R is: I Consider the change of variables: = 1₁₂ R -(x+y)² R = {(x, y) = R² : 0 ≤ y ≤ x, 2 ≤ x + y ≤3} u = x + y Y x dxdy V = 1. Draw the region R both in the x - y plane and in the u- v plane. 2. Invert the system writing the coordinates and y as function of u and v. 3. Use the change of variables from x - y to u - v to solve the integral I.
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