Calculus 3 Lesson 69: Center of Mass, Moments, & Inertia for 3D Solids

Apr 21, 2026

Hi there! Today I have released Lesson 69 of my Calculus 3 series. In this lesson we learn about an application of triple integrals!

In particular you will learn:

  1. How to find the mass of a solid 3D region
  2. How to find the first moments and center of mass of a solid 3D region
  3. How to find the moments of inertia of a solid 3D region

The unit on multiple integration is almost done! The next lesson will be the final lesson in the unit, where you will learn about Jacobians and changing variables of double integrals. After that I'll be moving right into the last unit with vector fields and line integrals. A lot to look forward to!

Until next time,

- Josh

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