Definition of integral

The word "integral" has its roots in the field of mathematics and has come to have broader meaning in various disciplines. In mathematics, an integral represents a definite or indefinite sum, usually of functions. In economics and cognitive psychology, it refers to the idea that various parts or factors contribute to the whole, such that the whole cannot be fully understood by examining any single part in isolation. The term "integral" comes from the Latin term intāgrālis, meaning "whole" or "unbroken." In the Renaissance, the term was used to describe a perfect mathematical shape that could be integrated or "put back together," such as a vase or sculpture made from a single piece of marble. Later, in the 17th century, mathematicians Leibniz and Newton used the term to describe the sum of products of a function and its derivative, which for certain functions like the familiar "area under the curve" of a function, could be thought of as a whole that could be taken apart and reassembled through integration. In modern usage, the term is often used in a figurative sense, such as in the expression "an integral part of" in relation to a larger whole. Such usage can be traced back to the late 1800s, when the term "integral biology" was coined by the American paleontologist Othniel Charles Marsh to describe the notion that all biological phenomena could be understood as interconnected parts of a larger biological system. Today, the term continues to be used in various fields to emphasize the idea that things are connected as part of a larger whole and should be understood in that context.