TeXipedia

int

Represents mathematical integration in calculus and analysis, used to find areas, volumes, and accumulations of quantities.

Overview

Essential in mathematical notation across science and engineering, serving as the fundamental symbol for both definite and indefinite integration.

  • Commonly used to calculate areas under curves, volumes of solids, and work done by forces
  • Appears extensively in physics equations, particularly in mechanics and electromagnetics
  • Often combined with limits to form definite integrals
  • Frequently used with differential terms (dx, dy) to indicate the variable of integration
  • Can be modified with subscripts and superscripts for multiple integration

Examples

Basic indefinite integral of x squared.

∫x2 dx=x33+C\int x^2 \, dx = \frac{x^3}{3} + C 
\int x^2 \, dx = \frac{x^3}{3} + C

Definite integral with bounds.

∫01x3 dx=14\int_0^1 x^3 \, dx = \frac{1}{4} 
\int_0^1 x^3 \, dx = \frac{1}{4}

Double integral over a region.

∫01∫01xy dx dy=14\int_0^1 \int_0^1 xy \, dx \, dy = \frac{1}{4} 
\int_0^1 \int_0^1 xy \, dx \, dy = \frac{1}{4}