Determining the area under a curve, bounded by the x-axis and specified vertical lines, is a fundamental concept in calculus. This process, known as definite integration, allows for the precise calculation of the accumulated quantity represented by the function’s graph within the designated interval. For instance, if a graph represents velocity over time, calculating the area under the curve between two points in time yields the total displacement during that interval.
The significance of this technique extends across various scientific and engineering disciplines. It enables the computation of quantities such as work done by a force, probability in statistical distributions, and total revenue from a marginal revenue function. Historically, the development of this method was instrumental in solidifying the foundations of calculus and provided powerful tools for solving a wide array of problems that were previously intractable. These methods allow us to analyze real-world phenomena where continuous change is a key factor.
