Mr. Integral

THE BIG IDEA

Geometry and Physical Applications

What should each tiny piece contribute?

Before integrating, decide what a small slice represents and what weights it needs. The same accumulation idea produces areas, volumes, lengths, work and mass when the element is modeled correctly.

Begin the first lesson →See the lesson route ↓

4 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 with01Area & averages
  2. giving slices thickness produces02Volume slices
  3. following a curved boundary produces03Curve & surface elements
  4. adding force or density models04Physical weights

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 unit4 lessons
  1. 01Area Between Curves and Average ValuesSplit an interval where curves cross and distinguish average height from accumulated area.
  2. 02Volumes of RevolutionChoose disks, washers or cylindrical shells from the geometry of a rotated region.
  3. 03Arc Length and Surface AreaBuild length from small line segments and surface area from circular bands.
  4. 04Work, Density and Center of MassTranslate force and density models into integrals with consistent units.