Stage 37 · Beyond (Optional)

37.1.6 The Fundamental Theorem of Calculus

37.1 First Steps with the Definite Integral and the Fundamental Theorem of Calculus

Point 6 of 7

37.1.6 The Fundamental Theorem of Calculus

Core idea

Astonishingly, finding an area is just taking the difference of an antiderivative, ∫ₐᵇf = F(b) − F(a), so differentiation and integration undo each other.

Module goal. Starting from the picture of finding an area or adding things up, build the idea of the definite integral and bridge it to the derivative, so the differentiation you just learned flows naturally into integration.

eastmath.com · 37.1 First Steps with the Definite Integral and the Fundamental Theorem of Calculus · 37.1.6 The Fundamental Theorem of Calculus