## The Centroid of a Planar Region

The Centroid of a Planar Region
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Taught by Houston

### Meets NCTM Standards:

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Calculation of moments and centroids.
• What is a centroid?
• How do you find the centroid of a shape?
• What is the centroid of a circle, triangle, rectangle, or pentagon?
• What is a moment?
• What is the formula for the moment about the y-axis or x-axis of a region in the plane?
• How do you find the moment of a narrow strip?
• How do you find the moment of the region between two curves?
• How do you find the centroid of the region between two curves?
• How do you find the centroid of the region bounded by y = x and y = x^4?
• How do you find the centroid of the quarter-disk where x^2 + y^2 < R^2?
The lesson explains how to find the centroid for basic shapes, such as triangles, rectangles, and circles. Then, slightly more complicated shapes are examined. Moments about the axes are also defined, as well as their properties. Some really interesting shapes are used as examples, and the moments of the shape about the axes are used to find the centroid of the shape. Many example shapes that are used are regions between curves.
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Reviewed by MathVids Staff on December 20, 2008.  