Explanation Given: Assume that f and g be continuous and satisfy f ( x ) ≥ g ( x ) on the interval [ a , b ] . Description: Consider a thin plate of uniform density ρ that covers the region R between the graphs of y = f ( x ) and y = g ( x ) on the interval [ a , b ] . Then, The mass of R is: m = ρ ∫ a b [ f ( x ) − g ( x ) ] d x . The centroid of R is the point ( x − , y − ) such that, x − = M y m = ∫ a b x [ f ( x ) − g ( x ) ] d x ∫ a b [ f ( x ) − g ( x ) ] d x And y − = M x m = 1 2 ∫ a b [ [ f ( x ) ] 2 − [ g

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6, Problem 13PE

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To find: The formula for the mass and the centroid of a homogeneous lamina.

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Chapter 6, Problem 12PE

Chapter 6, Problem 14PE

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Chapter 6 Solutions

Calculus

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The formula for the mass and the centroid of a homogeneous lamina.

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Chapter 6 Solutions