Explanation Given : f ( x , y ) = e x − y , the triangle bounded by y = 0 , x = 1 and y = x . Calculation : Step 1: We must first find a point P ( a , b ) in the triangle D such that ∫ ∫ D e x − y d A = e a − b . 1 2 since the area of the triangle is 1.1 2 = 1 2 Step 2: We must first compute the double integral. The inequalities defining D as a vertically simple region are 0 ≤ x ≤ 1 , 0 ≤ y ≤ x Step 3: Therefore, ∫ ∫ D e x − y d A = ∫ 0 1 ∫ 0 x e x − y d y d x = ∫ 0 1 − e x − y | y = 0 x d x = ∫ 0 1 − ( e x − x − e x − 0 ) d x =

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.2, Problem 62E

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The verification for the Mean Value Theorem for Double Integrals for $f (x, y) = e^{x - y}$ on the triangle bounded by $y = 0$ , $x = 1$ and $y = x$ .

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Chapter 16.2, Problem 61E

Chapter 16.2, Problem 63E

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The verification for the Mean Value Theorem for Double Integrals for f ( x , y ) = e x − y on the triangle bounded by y = 0 , x = 1 and y = x .

Solution Summary: The author explains the verification for the Mean Value Theorem for Double Integrals for f (x, y) = e x

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The verification for the Mean Value Theorem for Double Integrals for $f (x, y) = e^{x - y}$ on the triangle bounded by $y = 0$ , $x = 1$ and $y = x$ .

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Chapter 16 Solutions

The verification for the Mean Value Theorem for Double Integrals for f ( x , y ) = e x − y on the triangle bounded by y = 0 , x = 1 and y = x .

Solution Summary: The author explains the verification for the Mean Value Theorem for Double Integrals for f (x, y) = e x

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The verification for the Mean Value Theorem for Double Integrals for f(x,y)=ex−y on the triangle bounded by y=0, x=1 and y=x.

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Chapter 16 Solutions

The verification for the Mean Value Theorem for Double Integrals for $f (x, y) = e^{x - y}$ on the triangle bounded by $y = 0$ , $x = 1$ and $y = x$ .