Calculus: We present formulas for the moments and center of mass of a planar lamina of uniform density rho. Examples considered are (a) a rectangle of height h and base b, (b) the upper half of the unit disk, and (c) the region between y=x and y=x^2-x from x=0 to x=1. For part (c), we also show how to obtain the center of mass by splitting the region in two pieces.

1. The Area between Two Curves 1
2. The Area between Two Curves 2
3. Example of Volume Using Cross Sectional Area
4. The Disk/Washer Method for Volume 1
5. The Disk/Washer Method for Volume 2
6. The Disk/Washer Method for Volume 3
7. The Shell Method for Volume 1
8. The Shell Method for Volume 2
9. The Shell Method for Volume 3
10. Formula for Arc Length 1
11. Formula for Arc Length 2
12. Formula for Arc Length 3
13. Arc Length Along Parabola 1: Base Case
14. Arc Length Along Parabola 2: Sinh Formula
15. Arc Length Along Parabola 3: Log Formula
16. Area of a Surface of Revolution
17. Moments and Center of Mass 1 - Point Masses on a Line
18. Moments and Center of Mass 2 - Point Masses in the Plane
19. Moments and Center of Mass 3 - Planar Lamina of Uniform Density
20. Moments and Center of Mass 4 - Integral Formula for Planar Lamina
21. Moments and Center of Mass 5 - Rod of Nonuniform Density

In this series, Dr. Bob applies the principles of integral calculus covered thus far to solve some practical problems, including: Area between two curves, Disk Method for Volume, Shell Method for Volume, moment, center, mass.