Explanation Given: G ( u , v ) = ( u + v 2 , u − v 2 ) R is the square with the vertices ( π , 0 ) , ( 2 π , π ) , ( π , 2 π ) , ( 0 , π ) Calculation: G ( u , v ) = ( u + v 2 , u − v 2 ) Thus, x = u + v 2 and y = u − v 2 So, u = x + y and v = x − y Since R is bounded by x + y = π , x + y = 3 π , x − y = − π , x − y = π , this gives π ≤ u ≤ 3 π , − π ≤ v ≤ π Then R is the image of D under the map G So, ∫ ∫ R ( ( x − y ) sin ( x + y ) ) 2 d x d y = ∫ π 3 π ∫ − π π f ( x ( u , v ) , y ( u ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16, Problem 58CRE

To determine

To calculate:

$\int \int_{R} {((x - y) \sin (x + y))}^{2} d x d y$

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Chapter 16, Problem 57CRE

Chapter 16, Problem 59CRE

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.1 - Prob. 45E Ch. 16.1 - Prob. 46E Ch. 16.1 - Prob. 47E Ch. 16.1 - Prob. 48E Ch. 16.1 - Prob. 49E Ch. 16.1 - Prob. 50E Ch. 16.1 - Prob. 51E Ch. 16.1 - Prob. 52E Ch. 16.1 - 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∫ ∫ R ( ( x − y ) sin ( x + y ) ) 2 d x d y

Solution Summary: The author explains how R is the square with the vertices ( , 0 ) and the image of D under the map G.

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To calculate: ∫∫R((x−y)sin(x+y))2dxdy

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Chapter 16 Solutions

To calculate:

$\int \int_{R} {((x - y) \sin (x + y))}^{2} d x d y$