underive

Underive is a term that refers to the process of reversing the steps of a derivative to find the original function. This process is also known as antidifferentiation or indefinite integration. The term "underive" is not a standard mathematical term, but it is used informally to describe the concept of finding the original function from its derivative.

The process of underiving involves finding a function F(x) such that its derivative F'(x) equals a given function f(x). This is denoted as:

F(x) = ∫ f(x) dx

The result of underiving is called an antiderivative or indefinite integral. Unlike definite integrals, which yield a specific numerical value, indefinite integrals yield a family of functions that differ by a constant. This constant is known as the constant of integration.

Underiving is a fundamental concept in calculus and is used in various applications, such as finding areas under curves, solving differential equations, and calculating volumes of solids of revolution. It is the inverse operation of differentiation, which is the process of finding the rate of change of a function.