Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid (x, y of D are 1 1 x = 2A x2 dy 2A . y2 dx where A is the area of D. Find the centroid of a quarter-circular region of radius a.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid (x, y) of D are
1.
O x2 dy
y = -
y2 dx
2A Ic
X =
2A Jc
where A is the area of D.
Find the centroid of a quarter-circular region of radius a.
(*. F) - [
Transcribed Image Text:Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid (x, y) of D are 1. O x2 dy y = - y2 dx 2A Ic X = 2A Jc where A is the area of D. Find the centroid of a quarter-circular region of radius a. (*. F) - [
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