Explanation Given : f ( x , y ) = x 2 y , Shaded domain D in the figure. Calculation : Step 1: We can describe the domain D as a vertically simple region. Find the equation of the line connecting the points (0, 2) and (4, 0) y − 0 = 2 − 0 0 − 4 ( x − 4 ) ⇒ y = − 1 2 x + 2 The domain is thus described as a vertically simple region by the inequalities. 0 ≤ x ≤ 4 , − 1 2 x + 2 ≤ y ≤ 2 Step 2: Using Theorem 2 to evaluate the double integral ∫ ∫ D x 2 y d A = ∫ 0 4 ∫ − x 2 + 2 2 x 2 y d y d x =

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 5E

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The double integral of $f (x, y) = x^{2} y$ over the shaded domain in the figure.

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Chapter 16.2, Problem 4E

Chapter 16.2, Problem 6E

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The double integral of f ( x , y ) = x 2 y over the shaded domain in the figure.

Solution Summary: The author explains the double integral of f (x, y ) = x 2 over the shaded domain in the figure.

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The double integral of $f (x, y) = x^{2} y$ over the shaded domain in the figure.

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Chapter 16 Solutions

The double integral of f ( x , y ) = x 2 y over the shaded domain in the figure.

Solution Summary: The author explains the double integral of f (x, y ) = x 2 over the shaded domain in the figure.

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The double integral of f(x,y)=x2y over the shaded domain in the figure.

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Chapter 16 Solutions

The double integral of $f (x, y) = x^{2} y$ over the shaded domain in the figure.