(a) Explanation Given: The given substitutions are u = 3 y − x and v = y − x . Calculation: Considering the region R with points ( 1 , 1 ) , ( 3 , 3 ) , ( 6 , 4 ) and ( 4 , 2 ) . The provided substitutions are u = 3 y − x and v = y − x . Thus, At the point ( 1 , 1 ) , the value of u is; u ( 1 , 1 ) = 3 ( 1 ) − 1 = 2 And, the value of v is; v ( 1 , 1 ) = 1 − 1 = 0 Therefore, the point ( 1 , 1 ) in x y − plane is mapped to the point ( 2 , 0 ) in u v − plane . At the point ( 3 , 3 ) , the value of u is; u ( 3 , 3 ) = 3 ( 3 ) − 3 = 9 − 3 = 6 And, the value of v is; v ( 3 , 3 ) = 3 − 3 = 0 So, the point ( 3 , 3 ) in x y − plane is mapped to the point ( 6 , 0 ) in u v − plane . At the point ( 6 , 4 ) , the value of u is; u ( 6 , 4 ) = 3 ( 4 ) − 6 = 6 And, the value of v is; v ( 6 , 4 ) = 4 − 6 = − 2 So, the point ( 6 , 4 ) in x y − plane is mapped to the point ( 6 , − 2 ) in u v − plane (b) To determine The substitutions of u = y − x and v = 3 y − x for the transformation from the region R to S and the provided figures are: .

11th Edition

ISBN: 9781337604789

Author: Larson

Publisher: Cengage

See similar textbooks

Videos

Question

Chapter 14.8, Problem 32E

(a)

To determine

The substitution of u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are:

.

(b)

To determine

The substitutions of u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are:

.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.8, Problem 31E

Chapter 14.8, Problem 33E

Students have asked these similar questions

Question 3. the given integral is convergent or divergent: Use the comparison test to determine whether or not * sin*(x + 1) 7x3 (a) |. d.x g8 + x4 + 1 -dx (b) 2.x4 + x + 1

-d.x tan x

Please send me the answer for this question in clear way.

Chapter 14 Solutions

Bundle: Llf Multivariable Calculus

Ch. 14.1 - CONCEPT CHECK Iterated Integral Explain what is...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The substitution of u = 3 y − x and v = y − x for the transformation from the region R to S and the provided figures are: .

Solution Summary: The author calculates the substitutions of u=3y-x and v=y based on the region transform from R to S.

Videos

The substitution of u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are:

.

The substitutions of u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are:

.

Want to see the full answer?

Chapter 14 Solutions

The substitution of u = 3 y − x and v = y − x for the transformation from the region R to S and the provided figures are: .

Solution Summary: The author calculates the substitutions of u=3y-x and v=y based on the region transform from R to S.

Videos

The substitution of u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are: .

The substitutions of u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are: .

Want to see the full answer?

Chapter 14 Solutions

The substitution of u=3y−x and v=y−x for the transformation from the region R to S and the provided figures are:

.

The substitutions of u=y−x and v=3y−x for the transformation from the region R to S and the provided figures are:

.