Explore Integral on MathWorld

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.

Integral 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.


Calculus: Calculus is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects.
Derivative: A derivative is the infinitesimal rate of change in a function with respect to one of its parameters.

Classroom Articles on Calculus I (Up to College Level)

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