Mr. Integral

THE BIG IDEA

Parametric and Polar Calculus

What if x is not the most useful input?

A parameter describes both coordinates through a common clock, while polar coordinates describe angle and distance. Follow how the curve is traced before computing slope, length or enclosed area.

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 with01Parametric motion
  2. angle and radius offer02Polar geometry
  3. combining representations supports03Method selection

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. 01Parametric Curves and MotionCompute tangent slopes, speed and distance when both coordinates depend on a parameter.
  2. 02Polar Curves, Area and LengthInterpret signed polar radii and select a parameter interval that traces a region once.
  3. 03Calculus II CheckpointChoose a method, state its conditions and check the result across integration, series and curves.