integrál

Integrál is a mathematical concept representing the area under a curve. It is the inverse operation of differentiation. The integral can be understood as the accumulation of infinitesimally small quantities.

There are two main types of integrals: indefinite and definite. An indefinite integral, also known as an antiderivative, results in a function. It represents the family of functions whose derivative is the given function. The indefinite integral is denoted by the integral symbol ∫ followed by the function and 'dx', indicating the variable of integration. For example, the indefinite integral of 2x is x² + C, where C is the constant of integration.

A definite integral, on the other hand, results in a numerical value. It is calculated over a specific interval [a, b] and represents the net area between the function's graph and the x-axis within that interval. The definite integral is written as ∫ from a to b of f(x) dx. The fundamental theorem of calculus establishes a connection between differentiation and definite integration, stating that the definite integral of a function from a to b can be found by evaluating its antiderivative at b and subtracting its value at a. Integrals have wide-ranging applications in physics, engineering, economics, and statistics, used for calculating areas, volumes, work, probabilities, and much more.