Mr. Integral

THE BIG IDEA

Improper and Numerical Integration

When is an integral meaningful, and when is an estimate reliable?

Some integrals need limits before they have a value. Others are best estimated from samples. Treat convergence and numerical error as separate questions, and make the assumptions behind each explicit.

Begin the first lesson →See the lesson route ↓

2 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 with01Infinite or singular bounds
  2. when exact evaluation is difficult, use02Finite approximations

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 unit2 lessons
  1. 01Improper Integrals and ConvergenceDefine unbounded integrals using separate limits and distinguish convergence from cancellation.
  2. 02Numerical Quadrature and Error BoundsCompute trapezoidal and Simpson approximations and interpret their smoothness-dependent error bounds.