CALCULUS Understanding Its Concepts and Methods

Centroid

The centroid of a region is the center of the region. The coordinates of the centroid are the average values of the coordinates of the points in the region. If the region is made of material of uniform density, then the centroid is called the center of mass or the center of gravity. The centroid of a triangle is the intersection of its medians.

The coordinates of the centroid of a
plane region * R * of
area *A* are given by
the double integrals:

The coordinates of the centroid of a
three-dimensional region * R * of
area *V* are given by
triple integrals:

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.