Explanation Given : f ( x , y ) = x y 2 , the triangle indicated in the below figure Calculation : Step 1: To find the inequalities defining the triangle as a horizontally simple region, we first find the inequalities of lines AB and BC: AB: y − 2 = 4 − 2 3 − 1 ( x − 1 ) ⇒ y − 2 = x − 1 ⇒ x = y − 1 BC: y − 2 = 4 − 2 3 − 5 ( x − 5 ) ⇒ y − 2 = 5 − x ⇒ x = 7 − y We obtain the following inequalities for the triangle 2 ≤ y ≤ 4 , y − 1 ≤ x ≤ 7 − y Step 2: The double integral f ( x , y ) = x y 2 over the triangle is the following iterated integral:

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 41E

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The value of the double integral $f (x, y) = \frac{x}{y^{2}}$ over the triangle indicated in the given figure (C).

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Chapter 16.2, Problem 40E

Chapter 16.2, Problem 42E

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The value of the double integral f ( x , y ) = x y 2 over the triangle indicated in the given figure (C).

Solution Summary: The author explains the value of the double integral f ( x, y ) = 1.84 over the triangle indicated in the given figure.

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The value of the double integral $f (x, y) = \frac{x}{y^{2}}$ over the triangle indicated in the given figure (C).

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Chapter 16 Solutions

The value of the double integral f ( x , y ) = x y 2 over the triangle indicated in the given figure (C).

Solution Summary: The author explains the value of the double integral f ( x, y ) = 1.84 over the triangle indicated in the given figure.

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The value of the double integral f(x,y)=xy2 over the triangle indicated in the given figure (C).

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Chapter 16 Solutions

The value of the double integral $f (x, y) = \frac{x}{y^{2}}$ over the triangle indicated in the given figure (C).