Explanation Given: The provided density of lamina is: ρ ( x , y ) = x y , where x ≥ 0 and 3 ≤ y ≤ 3 + 9 − x 2 . Formula used: Mass of planar lamina is: m = ∬ R ρ ( x , y ) d A The integral of, ∫ x n d x = x n + 1 n + 1 + c Calculation: Consider the density function ρ ( x , y ) = x y , where x ≥ 0 and 3 ≤ y ≤ 3 + 9 − x 2 . Here the limit of y is, 3 ≤ y ≤ 3 + 9 − x 2 which means that the region is bounded by the line y = 3 and equation y ≤ 3 + 9 − x 2 , it represents the region of a circle as the equation of circle is x 2 + y 2 = r 2 . So, compare y ≤ 3 + 9 − x 2 with the equation of circle is x 2 + y 2 = r 2 . It is found that the center is at 3 units in positive y direction and radius of circle is 3. Since, x ≥ 0 so the limits of x , is 0 ≤ x ≤ 3

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.4, Problem 6E

To determine

To calculate: The mass of the lamina described by the inequalities given that its density is

ρ(x,y)=xy, where x≥0 and 3≤y≤3+9−x2.

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Chapter 14.4, Problem 5E

Chapter 14.4, Problem 7E

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√√y Find the mass and the center of mass of the lamina with density 8(x, y) = grams/cm² and occupies the rectangular region 1≤x≤√3 and 1≤ y ≤4.

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Chapter 14 Solutions

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The mass of the lamina described by the inequalities given that its density is ρ ( x , y ) = x y , where x ≥ 0 and 3 ≤ y ≤ 3 + 9 − x 2 .

Solution Summary: The author calculates the mass of the lamina described by the inequalities given that its density is rho (x,y)=xy.

Concept explainers

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To calculate: The mass of the lamina described by the inequalities given that its density is

ρ(x,y)=xy, where x≥0 and 3≤y≤3+9−x2.

Want to see the full answer?

Chapter 14 Solutions

The mass of the lamina described by the inequalities given that its density is ρ ( x , y ) = x y , where x ≥ 0 and 3 ≤ y ≤ 3 + 9 − x 2 .

Solution Summary: The author calculates the mass of the lamina described by the inequalities given that its density is rho (x,y)=xy.

Concept explainers

Videos

To calculate: The mass of the lamina described by the inequalities given that its density is ρ(x,y)=xy, where x≥0 and 3≤y≤3+9−x2.

Want to see the full answer?

Chapter 14 Solutions

To calculate: The mass of the lamina described by the inequalities given that its density is

ρ(x,y)=xy, where x≥0 and 3≤y≤3+9−x2.