In these lessons, we will look at how to calculate the centroid or the center of mass of a region.

**Related Pages**

Centroid Of A Triangle

More Calculus Lessons

Looking for some Calculus help? We have a a series of free calculus videos that will explain the various concepts of calculus.

**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) = x^{2} + 4 and g(x) = 2x^{2}.

**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 = x^{2} and y = 8 - x^{2}

**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**

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 - x^{2} and below by the x-axis. Assume the density of the plate at the
point (x,y) is δ = 2x^{2}, which is twice the square of the distance from
the point to the y-axis.

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