---
id: mat-04-integrals
title: "Integrals: basics and the fundamental theorem"
---

# Integrals

## Antiderivative
An antiderivative is a function whose derivative is the integrand.

## Definite integral
A definite integral measures accumulated change and is interpreted as signed area under a curve.

## Fundamental theorem of calculus
The fundamental theorem connects derivatives and integrals:
- differentiation and accumulation are inverse operations (under suitable conditions)

## Basic integration rules
Rules include:
- linearity
- power rule for integrals (with n not equal to -1)
- integral of 1/x is ln|x|

## Substitution idea
Substitution changes variables to simplify the integrand when a composition structure appears.