Integral Calculus

Integrals are the inverse method of differentiation, thus integral calculus helps in finding the anti-derivatives of a function. These anti-derivatives are also called the integrals of the function.
Integrals are the values of the function found by the process of integration(a way of uniting the part to find a whole).

  • The process of finding the anti-derivative of a function is called integration.
  • The inverse process of finding derivatives is finding the integrals.
  • The integral of a function represents a family of curves.
  • integration is the inverse of differentiation.
  • Integration is the process of finding the area of the region under the curve.
  • integral calculus deals with the problems like determining the area of the region bounded by the graph of the functions
  • Integrals can be solved with help of various formulas and methods like substitution, partial fraction and integration by parts

Definite Integrals

The definite integral of a function between the limits a to b(interval ) is denoted as:

where is the antiderivative of .

Indefinite Integral

In Indefinite Integral, the integrals do not have a pre-existing value of limits.

Components of indefinite integral:

  • : Integration of with respect to
  • often called “Integral of” stands for Sum and simply means “The whole of”
  • often called “An element of …” simply means “a tiny bit of given variable”
  • : The integrand
  • : The variable of integration
  • : The antiderivative of the function.
  • : The constant of integration


integral calculus where is a constant

Derivatives Integrals
, where