Definite Integrals
A definite integral is a mathematical concept used to calculate the area under a curve defined by a function over a specific interval. It is represented as ∫[a, b] f(x) dx, where f(x) is the function, and a and b are the limits of integration. The result of a definite integral is a numerical value that represents the total accumulation of the function's values between these two points.
Definite integrals are fundamental in various fields, including physics, engineering, and economics, as they help in determining quantities like distance, area, and total accumulated change. The process of finding a definite integral often involves using the Fundamental Theorem of Calculus, which connects differentiation and integration, allowing for easier computation of these areas.