Math Playground
Calculus

Fundamental theorem of calculus

Differentiation and integration are inverses — the link that ties everything together.

Differentiation and integration are inverses — the deepest result in calculus.

Two parts

  • Part 1: d/dx [∫ₐˣ f(t) dt] = f(x).
  • Part 2: ∫ₐᵇ f(x) dx = F(b) − F(a), where F' = f.