 # Calculate the Centroid or Center of Mass of a Region

Looking for some Calculus help?
We have a a series of free calculus videos that will explain the various concepts of calculus. In these lessons, we will look at how to calculate the centroid or the center of mass of a region.

Related Topics:
More Calculus Lessons

Formulas to find the moments and center of mass of a region
The following table gives the formulas for the moments and center of mass of a region. Scroll down the page for examples and solutions on how to use the formulas for different applications. Find the Centroid of a Triangular Region on the Coordinate Plane
How to determine the centroid of a triangular region with uniform density?
Example:
Find the centroid of the triangle with vertices (0,0), (3,0), (0,5).
Find the Centroid of a Bounded Region Involving Two Quadratic Functions How to determine the centroid of a region bounded by two quadratic functions with uniform density?
Example:
Find the centroid of the region with uniform density bounded by the graphs of the functions f(x) = x2 + 4 and g(x) = 2x2.

How to find the center of mass of a region using calculus?
Centroids / Centers of Mass - Part 1 of 2
This video will give the formula and calculate part 1 of an example.
Example:
Find centroid of region bonded by the two curves, y = x2 and y = 8 - x2 Centroids / Centers of Mass - Part 2 of 2.
This video gives part 2 of the problem of finding the centroids of a region. How to find the center of mass of a thin plate using calculus?
Center of Mass / Centroid, Example 1, Part 1
Example:
Find the center of mass of the indicated region. Center of Mass / Centroid, Example 1, Part 2
We continue with part 2 of finding the center of mass of a thin plate using calculus.

How to use integration to find moments and center of mass of a thin plate?
Moments and Center of Mass - Part 1 Moments and Center of Mass Part 2
Calculating the moments and center of mass of a thin plate with integration. Center of Mass of a Thin Plate Example:
Find the center of mass of a thin plate covering the region bounded above by the parabola y = 4 - x2 and below by the x-axis. Assume the density of the plate at the point (x,y) is δ = 2x2, which is twice the square of the distance from the point to the y-axis.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  