Integration in maths is the process of combining tiny parts to find a whole. In calculus, it is the inverse of differentiation, and it is often used to find areas under curves, total distance from speed, or other accumulated quantities.

Simple meaning

Think of integration like adding up many very small pieces until they make a full amount. That is why it is useful when a shape or quantity is too complex to measure directly.

Main ideas

  • Indefinite integration gives a family of functions called antiderivatives, usually written with a constant CCC.
  • Definite integration gives a specific numerical value, often representing the area under a curve between two limits.
  • Integration and differentiation are linked by the Fundamental Theorem of Calculus.

Quick example

If the derivative of a function is 2x2x2x, then one integral is x2+Cx^2+Cx2+C. That means integration “reverses” the differentiation step.

Where it is used

Integration is used in physics, engineering, economics, and statistics for things like displacement, volume, growth, and probability.

Short takeaway

Integration is basically adding continuously rather than adding in separate chunks, and it is one of the core ideas of calculus.

Would you like a very simple graph-based example of integration?