Fundamental Theorems of Calculus

Explore FundamentalTheoremsofCalculus on MathWorld

The fundamental theorems of calculus are deep results in analysis that express definite integrals of continuous functions in terms of antiderivatives.

Fundamental theorems of calculus is a college-level concept that would be first encountered in a Calculus I course. It is an Advanced Placement Calculus AB topic and is listed in the California State Standards for Calculus.


Derivative: A derivative is the infinitesimal rate of change in a function with respect to one of its parameters.
Integral: An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals and derivatives are the fundamental objects of calculus.

Classroom Articles on Calculus I (Up to College Level)

  • Calculus
  • Inflection Point
  • Chain Rule
  • Intermediate Value Theorem
  • Continuous Function
  • Limit
  • Critical Point
  • Maximum
  • Definite Integral
  • Mean-Value Theorem
  • Discontinuity
  • Minimum
  • Extreme Value Theorem
  • Newton's Method
  • First Derivative Test
  • Riemann Sum
  • Implicit Differentiation
  • Second Derivative Test
  • Indefinite Integral