Explanation Given: The plate in Figure 10 and the mass density is f ( x , y ) = x 2 / ( x 2 + y 2 ) g/cm 2 Formula used: The total mass of a region D with a given mass density f ( x , y ) is the solution of the integration ∬ D f ( x , y ) d A (in 2-dimention) where d A is an elementary area of the region D . Calculation: Here the region is the given by Figure 10, that is a region bounded by y = 0 ; x = 10 and x 2 + y 2 = 20 2 If we change it in polar co-ordinates then x = r cos θ ; y = r sin θ and d A = d x d y = r d r d θ Also x = 10 will be r = 10 cos θ and 10 / cos θ ≤ r ≤ 20 ; 0 ≤ θ ≤ π 3 So, the integration will be ∬ D f ( x , y ) d A = ∬ D x 2 / ( x 2 + y 2 ) d x d y = ∫ 0 π 3 ∫ 10 /

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.5, Problem 8E

To determine

The total mass of a plate assuming a mass density $f (x, y)$

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Chapter 16.5, Problem 7E

Chapter 16.5, Problem 9E

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Chapter 16 Solutions

Calculus - Standalone book

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