Riemann sums, antiderivatives and the fundamental theorem of calculus explained with animations, real life stories and short, runnable Python.

The Fundamental Theorem of Calculus, Explained Like a Friend Would

See why the area grows at the curve’s height, why plus C cancels, and where it finally breaks.

Watch the rectangles shrink until the area is exact, which is the whole idea of an integral in one loop.

Your Car Dashboard Has Been Doing Calculus Right in Front of You

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Next time you’re in a car, look at the dashboard. There are two numbers there that most people never think about together.

One is the speedometer. It tells you how fast you’re going right now, this second. The other is the odometer, the counter that tells you how far the car has travelled in total, ever.

Those two numbers are the two halves of calculus. The speedometer shows a rate. The odometer shows a running total, every kilometre added up since the car left the factory. Nobody mentions this when you’re learning to drive.