Find the mass and center of mass of the lamina that occupies the region D and has the given density function p. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); p(x, y) = 4(x + y)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find the mass and center of mass of the lamina that occupies the region \( D \) and has the given density function \( \rho \).

\( D \) is the triangular region with vertices \( (0, 0), (2, 1), (0, 3) \); \( \rho(x, y) = 4(x + y) \)

\[
m = \boxed{\phantom{a}}
\]

\[
(\bar{x}, \bar{y}) = \left( \boxed{\phantom{a}} \right)
\]
Transcribed Image Text:Find the mass and center of mass of the lamina that occupies the region \( D \) and has the given density function \( \rho \). \( D \) is the triangular region with vertices \( (0, 0), (2, 1), (0, 3) \); \( \rho(x, y) = 4(x + y) \) \[ m = \boxed{\phantom{a}} \] \[ (\bar{x}, \bar{y}) = \left( \boxed{\phantom{a}} \right) \]
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