What is the definition of integration?

• A. Differentiation
• B. Subtraction
• C. An operation used in calculus whereby the integral of a function is determined
• D. Multiplication

Answer: (C)

Integration is the operation in calculus that determines the integral of a function, capturing the idea of accumulation or total quantity. It includes finding an antiderivative (the indefinite integral) and computing a definite integral that represents something gathered over an interval, such as area under a curve or total distance from a rate function. For example, if velocity describes how position changes, integrating velocity over time yields the total distance traveled. This process is the inverse of differentiation, which finds the rate of change. In contrast, subtraction and multiplication are basic arithmetic operations and do not define what integration means.