integrálját

Integrál is a term used in mathematics, often referring to the concept of integration. Integration is a fundamental operation in calculus, alongside differentiation. It is essentially the inverse process of differentiation. Broadly, integration can be understood as the process of finding the area under a curve.

There are two main types of integrals: indefinite and definite. An indefinite integral, also known as an antiderivative, represents a family of functions whose derivative is the given function. It is denoted by a symbol like ∫f(x) dx and includes an arbitrary constant of integration, C. A definite integral, on the other hand, calculates a specific numerical value. It represents the net area between a function's graph and the x-axis over a specified interval, denoted as ∫[a,b] f(x) dx.

The concept of integration has wide-ranging applications in various scientific and engineering fields. It is used to calculate volumes, lengths of curves, work done by a force, probabilities, and much more. The development of integral calculus is often attributed to Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, though earlier ideas existed. It is a cornerstone of modern mathematics and its applications.