Integral
Integral is a fundamental concept in mathematics, specifically in the field of calculus. It is used to calculate the area under a curve, the length of a curve, and the volume of a solid of revolution. The process of finding integrals is called integration.
Definition
An integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with derivative, integral is the fundamental operation in calculus.
Types of Integrals
There are two types of integrals: definite integral and indefinite integral. A definite integral has actual numbers as limits while an indefinite integral has no limits.
Definite Integral
A definite integral of a function can be represented as the signed area of the region bounded by its graph. The process of finding definite integrals is called integration.
Indefinite Integral
An indefinite integral, also known as an antiderivative, represents a family of functions. The process of finding indefinite integrals is called integration.
Applications
Integrals are used in many practical applications. They are used in physics to calculate the center of mass, the mass of an object, the moment of inertia, and the work done by a force. In engineering, they are used to calculate the length of a curve, the area of a surface, and the volume of a solid.
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