Fundamental Theorem of Calculus

Calculus · 1670

Equation: ∫_a^b f′(x) dx = f(b) − f(a)
Field: Calculus
Symbols: f′ a rate of change · ∫_a^b … dx the total accumulated between a and b · f(b) − f(a) the net change
Year: 1670

Significance

Adding up a rate of change over an interval gives the total change — so integration undoes differentiation, and the area under a velocity graph is the distance travelled. Barrow had the geometric version in 1670; his student Newton and, separately, Leibniz turned it into a method. Kinematics, the rocket equation and every 'work is the integral of force' rest on it.

Requires

Derivative

Required By

Stokes' Theorem Divergence Theorem Kinematic Equations Work Tsiolkovsky Rocket Equation Euler–Lagrange Equation

Referenced by

equation

Derivative Divergence Theorem Euler–Lagrange Equation Kinematic Equations Stokes' Theorem Tsiolkovsky Rocket Equation Work

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.