Explanation Given: The function is z e 2 x + y here 0 ≤ x ≤ 2 , 0 ≤ y ≤ 3 and 0 ≤ z ≤ 4 . Calculation: Consider the integral I = ∬ S z e 2 x + y d S . Evaluate the integral on the plane x = 0 as; I 1 = ∫ y = 0 y = 3 ∫ z = 0 z = 4 z e y d z d y = ∫ y = 0 y = 3 [ z 2 2 ] z = 0 z = 4 e y d y = ∫ y = 0 y = 3 [ 4 2 2 − 0 2 2 ] e y d y = 8 ∫ y = 0 y = 3 e y d y Further calculation shows that; 8 ∫ y = 0 y = 3 e y d y = 8 [ e y ] y = 0 y = 3 = 8 ( e 3 − 1 ) Evaluate the integral on the plane x = 2 as; I 2 = ∫ y = 0 y = 3 ∫ z = 0 z = 4 z e 4 + y d z d y = ∫ y = 0 y = 3 [ z 2 2 ] z = 0 z = 4 e 4 + y d y = ∫ y = 0 y = 3 [ 4 2 2 − 0 2 2 ] e y d y = 8 ∫ y = 0 y = 3 e 4 + y d y Further calculation shows that; 8 ∫ y = 0 y = 3 e 4 + y d y = 8 [ e 4 + y ] y = 0 y = 3 = 8 ( e 7 − e 3 ) Evaluate the integral on the plane y = 0 as; I 3 = ∫ x = 0 x = 2 ∫ z = 0 z = 4 z e 2 x d z d x = ∫ x = 0 x = 2 [ z 2 2 ] z = 0 z = 4 e 2 x d x = ∫ x = 0 x = 2 [ 4 2 2 − 0 2 2 ] e 2 x d x = 8 ∫ x = 0 x = 2 e 2 x d y Further calculation shows that; 8 ∫ x = 0 x = 2 e 2 x d y = 4 [ e 2 x ] x = 0 x = 2 = 4 ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.4, Problem 38E

To determine

The integral of $z e^{2 x + y}$ over the surface of box.

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Chapter 17.4, Problem 37E

Chapter 17.4, Problem 39E

Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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Prob. 13E Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - Prob. 18E Ch. 17.3 - Prob. 19E Ch. 17.3 - Prob. 20E Ch. 17.3 - Prob. 21E Ch. 17.3 - Prob. 22E Ch. 17.3 - Prob. 23E Ch. 17.3 - Prob. 24E Ch. 17.3 - Prob. 25E Ch. 17.3 - Prob. 26E Ch. 17.3 - Prob. 27E Ch. 17.3 - Prob. 28E Ch. 17.3 - Prob. 29E Ch. 17.3 - Prob. 30E Ch. 17.3 - Prob. 31E Ch. 17.3 - Prob. 32E Ch. 17.3 - Prob. 33E Ch. 17.3 - Prob. 34E Ch. 17.3 - Prob. 35E Ch. 17.4 - Prob. 1PQ Ch. 17.4 - Prob. 2PQ Ch. 17.4 - Prob. 3PQ Ch. 17.4 - Prob. 4PQ Ch. 17.4 - Prob. 5PQ Ch. 17.4 - Prob. 6PQ Ch. 17.4 - Prob. 1E Ch. 17.4 - Prob. 2E Ch. 17.4 - Prob. 3E Ch. 17.4 - Prob. 4E Ch. 17.4 - Prob. 5E Ch. 17.4 - Prob. 6E Ch. 17.4 - Prob. 7E Ch. 17.4 - Prob. 8E Ch. 17.4 - Prob. 9E Ch. 17.4 - Prob. 10E Ch. 17.4 - Prob. 11E Ch. 17.4 - Prob. 12E Ch. 17.4 - Prob. 13E Ch. 17.4 - Prob. 14E Ch. 17.4 - Prob. 15E Ch. 17.4 - Prob. 16E Ch. 17.4 - Prob. 17E Ch. 17.4 - Prob. 18E Ch. 17.4 - Prob. 19E Ch. 17.4 - Prob. 20E Ch. 17.4 - 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The integral of z e 2 x + y over the surface of box.

Solution Summary: The author explains the integral of z e 2 x + y over the surface of box.

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The integral of $z e^{2 x + y}$ over the surface of box.

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Chapter 17 Solutions

The integral of z e 2 x + y over the surface of box.

Solution Summary: The author explains the integral of z e 2 x + y over the surface of box.

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The integral of ze2x+y over the surface of box.

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Chapter 17 Solutions

The integral of $z e^{2 x + y}$ over the surface of box.