Mr. Integral

THE BIG IDEA

The Integral

How do tiny changes add up to a total?

Start with antiderivatives and finite sums. The Fundamental Theorem then connects accumulated change with instantaneous rate, letting you calculate totals while keeping their physical meaning.

Begin the first lesson →See the lesson route ↓

5 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 with01Antiderivatives
  2. summing small contributions describes02Accumulation
  3. connecting rate and total gives03The Fundamental Theorem
  4. interpreting the integral yields04Net change

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 unit5 lessons
  1. 01Antiderivatives and Initial ValuesRecover a family of functions from a rate and use one value to select a member.
  2. 02Riemann Sums and AccumulationConstruct weighted sums from a partition and distinguish their finite approximation from an integral.
  3. 03Definite Integrals and the Fundamental TheoremConnect accumulated change to antiderivatives and differentiate a variable-limit integral.
  4. 04Substitution and Transformed BoundsRecognize a composition and change the variable, differential and bounds consistently.
  5. 05Net Change, Distance and a Calculus I CheckpointCombine derivatives and integrals to interpret a changing quantity and check your course-level reasoning.