Explanation In order to obtain the double integral, integrate the inner integral first. ∫ 1 2 ( 3 y + 2 x y ) d x = [ 3 y x + x 2 y ] 1 2 = [ 3 y ( 2 ) + ( 2 ) 2 y ] − [ 3 y ( 1 ) + ( 1 ) 2 y ] = [ 6 y + 4 y ] − [ 3 y + y ] = 10 y − 4 y That is, ∫ 1 2 ( 3 y + 2 x y ) d x = 6 y . Now, obtain the outer integral with the help of the result of inner integral as follows

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 29, Problem 27RE

To determine

To evaluate: The double integral ∫02∫12(3y−2xy)dxdy.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 29, Problem 26RE

Chapter 29, Problem 28RE

Students have asked these similar questions

5. (a) State the Residue Theorem. Your answer should include all the conditions required for the theorem to hold. (4 marks) (b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the anti-clockwise direction. Evaluate に dz. You must check all of the conditions of any results that you use. (5 marks) (c) Evaluate L You must check all of the conditions of any results that you use. ཙ x sin(Tx) x²+2x+5 da. (11 marks)

3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula for L(y). (1 mark) (b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a contour. Suppose there exists a finite real number M such that |f(z)| < M for all z in the image of y. Prove that < ||, f(z)dz| ≤ ML(y). (3 marks) (c) State and prove Liouville's theorem. You may use Cauchy's integral formula without proof. (d) Let R0. Let w € C. Let (10 marks) U = { z Є C : | z − w| < R} . Let f UC be a holomorphic function such that 0 < |ƒ(w)| < |f(z)| for all z Є U. Show, using the local maximum modulus principle, that f is constant. (6 marks)

3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M a simple module? (b) State and prove Schur's Lemma for simple modules. (c) Let AM(K) and M = K" the natural A-module. (i) Show that M is a simple K-module. (ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a is a matrix in the centre of M, (K). [Recall that the centre, Z(M,(K)) == {a Mn(K) | ab M,,(K)}.] = ba for all bЄ (iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~ K as K-algebras. Is this consistent with Schur's lemma?

Chapter 29 Solutions

Basic Technical Mathematics

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

Ch. 29.1 - Prob. 10E Ch. 29.1 - Prob. 11E Ch. 29.1 - Prob. 12E Ch. 29.1 - Prob. 13E Ch. 29.1 - Prob. 14E Ch. 29.1 - Prob. 15E Ch. 29.1 - Prob. 16E Ch. 29.1 - Prob. 17E Ch. 29.1 - Prob. 18E Ch. 29.1 - Prob. 19E Ch. 29.1 - Prob. 20E Ch. 29.1 - Prob. 21E Ch. 29.1 - Prob. 22E Ch. 29.1 - Prob. 23E Ch. 29.1 - Prob. 24E Ch. 29.1 - Prob. 25E Ch. 29.1 - Prob. 26E Ch. 29.1 - Prob. 27E Ch. 29.1 - Prob. 28E Ch. 29.1 - Prob. 29E Ch. 29.1 - Prob. 30E Ch. 29.1 - Prob. 31E Ch. 29.1 - Prob. 32E Ch. 29.1 - Prob. 33E Ch. 29.1 - Prob. 34E Ch. 29.1 - Prob. 35E Ch. 29.1 - Prob. 36E Ch. 29.1 - Prob. 37E Ch. 29.1 - Prob. 38E Ch. 29.1 - Prob. 39E Ch. 29.1 - Prob. 40E Ch. 29.1 - Prob. 41E Ch. 29.1 - Prob. 42E Ch. 29.1 - Prob. 43E Ch. 29.1 - Prob. 44E Ch. 29.2 - Prob. 1PE Ch. 29.2 - Prob. 2PE Ch. 29.2 - Prob. 1E Ch. 29.2 - Prob. 2E Ch. 29.2 - Prob. 3E Ch. 29.2 - Prob. 4E Ch. 29.2 - Prob. 5E Ch. 29.2 - Prob. 6E Ch. 29.2 - Prob. 7E Ch. 29.2 - Prob. 8E Ch. 29.2 - Prob. 9E Ch. 29.2 - Prob. 10E Ch. 29.2 - Prob. 11E Ch. 29.2 - Prob. 12E Ch. 29.2 - Prob. 13E Ch. 29.2 - Prob. 14E Ch. 29.2 - Prob. 15E Ch. 29.2 - Prob. 16E Ch. 29.2 - Prob. 17E Ch. 29.2 - Prob. 18E Ch. 29.2 - Prob. 19E Ch. 29.2 - Prob. 20E Ch. 29.2 - Prob. 21E Ch. 29.2 - Prob. 22E Ch. 29.2 - Prob. 23E Ch. 29.2 - Prob. 24E Ch. 29.2 - Prob. 25E Ch. 29.2 - Prob. 26E Ch. 29.2 - Prob. 27E Ch. 29.2 - Prob. 28E Ch. 29.2 - Prob. 29E Ch. 29.2 - Prob. 30E Ch. 29.2 - Prob. 31E Ch. 29.2 - Prob. 32E Ch. 29.2 - Prob. 33E Ch. 29.2 - Prob. 34E Ch. 29.2 - Prob. 35E Ch. 29.2 - Prob. 36E Ch. 29.2 - Prob. 37E Ch. 29.2 - Prob. 38E Ch. 29.2 - Prob. 39E Ch. 29.2 - Prob. 40E Ch. 29.2 - Prob. 41E Ch. 29.2 - Prob. 42E Ch. 29.2 - Prob. 43E Ch. 29.2 - Prob. 44E Ch. 29.2 - Prob. 45E Ch. 29.2 - Prob. 46E Ch. 29.3 - If z = 4x2 + x sin y, find ∂z/∂x and ∂z/∂y. Ch. 29.3 - Prob. 2PE Ch. 29.3 - Prob. 1E Ch. 29.3 - Prob. 2E Ch. 29.3 - Prob. 3E Ch. 29.3 - Prob. 4E Ch. 29.3 - Prob. 5E Ch. 29.3 - Prob. 6E Ch. 29.3 - Prob. 7E Ch. 29.3 - Prob. 8E Ch. 29.3 - Prob. 9E Ch. 29.3 - Prob. 10E Ch. 29.3 - Prob. 11E Ch. 29.3 - Prob. 12E Ch. 29.3 - Prob. 13E Ch. 29.3 - Prob. 14E Ch. 29.3 - Prob. 15E Ch. 29.3 - Prob. 16E Ch. 29.3 - Prob. 17E Ch. 29.3 - Prob. 18E Ch. 29.3 - Prob. 19E Ch. 29.3 - Prob. 20E Ch. 29.3 - Prob. 21E Ch. 29.3 - Prob. 22E Ch. 29.3 - Prob. 23E Ch. 29.3 - Prob. 24E Ch. 29.3 - Prob. 25E Ch. 29.3 - Prob. 26E Ch. 29.3 - Prob. 27E Ch. 29.3 - Prob. 28E Ch. 29.3 - Prob. 29E Ch. 29.3 - Prob. 30E Ch. 29.3 - Prob. 31E Ch. 29.3 - Prob. 32E Ch. 29.3 - Prob. 33E Ch. 29.3 - Prob. 34E Ch. 29.3 - Prob. 35E Ch. 29.3 - Prob. 36E Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - Prob. 39E Ch. 29.3 - Prob. 40E Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - Prob. 42E Ch. 29.3 - Prob. 43E Ch. 29.3 - Prob. 44E Ch. 29.3 - Prob. 45E Ch. 29.3 - Prob. 46E Ch. 29.3 - Prob. 47E Ch. 29.3 - Prob. 48E Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.4 - Prob. 1PE Ch. 29.4 - Prob. 1E Ch. 29.4 - Prob. 2E Ch. 29.4 - Prob. 3E Ch. 29.4 - Prob. 4E Ch. 29.4 - Prob. 5E Ch. 29.4 - In Exercises 5–18, evaluate the given double...Ch. 29.4 - Prob. 7E Ch. 29.4 - Prob. 8E Ch. 29.4 - Prob. 9E Ch. 29.4 - Prob. 10E Ch. 29.4 - Prob. 11E Ch. 29.4 - Prob. 12E Ch. 29.4 - Prob. 13E Ch. 29.4 - Prob. 14E Ch. 29.4 - Prob. 15E Ch. 29.4 - Prob. 16E Ch. 29.4 - Prob. 17E Ch. 29.4 - Prob. 18E Ch. 29.4 - Prob. 19E Ch. 29.4 - Prob. 20E Ch. 29.4 - Prob. 21E Ch. 29.4 - Prob. 22E Ch. 29.4 - Prob. 23E Ch. 29.4 - Prob. 24E Ch. 29.4 - Prob. 25E Ch. 29.4 - Prob. 26E Ch. 29.4 - Prob. 27E Ch. 29.4 - Prob. 28E Ch. 29.4 - Prob. 29E Ch. 29.4 - Prob. 30E Ch. 29.4 - Prob. 31E Ch. 29.4 - Prob. 32E Ch. 29.4 - Prob. 33E Ch. 29.4 - Prob. 34E Ch. 29 - Prob. 1RE Ch. 29 - Prob. 2RE Ch. 29 - Prob. 3RE Ch. 29 - Prob. 4RE Ch. 29 - Prob. 5RE Ch. 29 - Prob. 6RE Ch. 29 - Prob. 7RE Ch. 29 - Prob. 8RE Ch. 29 - Prob. 9RE Ch. 29 - Prob. 10RE Ch. 29 - Prob. 11RE Ch. 29 - Prob. 12RE Ch. 29 - Prob. 13RE Ch. 29 - Prob. 14RE Ch. 29 - Prob. 15RE Ch. 29 - Prob. 16RE Ch. 29 - Prob. 17RE Ch. 29 - Prob. 18RE Ch. 29 - Prob. 19RE Ch. 29 - Prob. 20RE Ch. 29 - Prob. 21RE Ch. 29 - Prob. 22RE Ch. 29 - Prob. 23RE Ch. 29 - Prob. 24RE Ch. 29 - Prob. 25RE Ch. 29 - Prob. 26RE Ch. 29 - Prob. 27RE Ch. 29 - Prob. 28RE Ch. 29 - Prob. 29RE Ch. 29 - Prob. 30RE Ch. 29 - Prob. 31RE Ch. 29 - Prob. 32RE Ch. 29 - Prob. 33RE Ch. 29 - Prob. 34RE Ch. 29 - Prob. 35RE Ch. 29 - Prob. 36RE Ch. 29 - Prob. 37RE Ch. 29 - Prob. 38RE Ch. 29 - Prob. 39RE Ch. 29 - Prob. 40RE Ch. 29 - Prob. 41RE Ch. 29 - Prob. 42RE Ch. 29 - Prob. 43RE Ch. 29 - Prob. 44RE Ch. 29 - Prob. 45RE Ch. 29 - Prob. 46RE Ch. 29 - Prob. 47RE Ch. 29 - Prob. 48RE Ch. 29 - Prob. 49RE Ch. 29 - Prob. 50RE Ch. 29 - Prob. 51RE Ch. 29 - Prob. 52RE Ch. 29 - Prob. 53RE Ch. 29 - Prob. 54RE Ch. 29 - Prob. 55RE Ch. 29 - Prob. 1PT Ch. 29 - Prob. 2PT Ch. 29 - Prob. 3PT Ch. 29 - Prob. 4PT Ch. 29 - Prob. 5PT Ch. 29 - Prob. 6PT Ch. 29 - Prob. 7PT Ch. 29 - Prob. 8PT

Knowledge Booster

Learn more about

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

The double integral ∫ 0 2 ∫ 1 2 ( 3 y − 2 x y ) d x d y .

Videos

To evaluate: The double integral ∫02∫12(3y−2xy)dxdy.

Want to see the full answer?

Chapter 29 Solutions