Mr. Integral

THE BIG IDEA

Triple Integrals

How do shape and density determine a solid’s totals?

Describe a solid using nested bounds, then choose coordinates adapted to its symmetry. Density and moment weights turn the same volume element into different physical measurements.

Begin the first lesson →See the lesson route ↓

3 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Solid bounds
  2. symmetry simplifies with02Adapted coordinates
  3. weighting each volume gives03Mass & moments

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit3 lessons
  1. 01Triple Integrals and Solid BoundsDescribe a solid with nested inequalities and integrate volume-weighted quantities.
  2. 02Cylindrical and Spherical CoordinatesChoose coordinates adapted to a solid and include the correct volume scaling.
  3. 03Density, Centers of Mass and Moments of InertiaWeight geometric contributions by density and distinguish first moments from rotational inertia.