Solve the following integral: I = y³ dædy R where the region R is: 1 R= { (x, y) E R² : ;x < y° < 2x,¬ < xy < 1 Consider the change of variables: y? U= v = xY 1. Draw the region R both in the x – y plane and in the u – v plane. 2. Invert the system writing the coordinates x 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: I = y³ dædy R where the region R is: 1 R= { (x, y) E R² : ;x < y° < 2x,¬ < xy < 1 Consider the change of variables: y? U= v = xY 1. Draw the region R both in the x – y plane and in the u – v plane. 2. Invert the system writing the coordinates x 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Transcribed Image Text:a) Solve the following integral:
I =
y³ dædy
R
where the region R is:
{ (x, y) E R?
1
x < y° < 2x,
R :
:
Consider the change of variables:
Su= ²
y?
v = xy
1. Draw the region R both in the x – y plane and in the u
v plane.
2. Invert the system writing the coordinates x 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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