Fundamental Theorem of Calculus

Differentiation and integration are inverse operations — the theorem that ties the two halves of calculus together.

Specifications & Metrics

proved

Newton and Leibniz, 1660s–1670s; rigorous form 19th century

Core Principles & Analysis

• Part one says an accumulation function's derivative recovers the original function.
• Part two evaluates definite integrals from any antiderivative — computation at a stroke.
• Newton and Leibniz's priority war over it split European mathematics for a century.