The Definite Integral

The definite integral is a fundamental concept in calculus that represents the accumulation of quantities over an interval. It finds extensive applications in various fields, including physics, engineering, economics, and statistics. Defined as the limit of Riemann sums, the definite integral computes the net area under a curve bounded by the x-axis within a specific interval. This mathematical tool provides precise methods for determining total quantities, such as distance traveled, area enclosed, or accumulated value over time. Understanding the definite integral is essential for solving problems involving continuous change and analyzing real-world phenomena with quantitative precision.