The definite integral represents the area under a curve on a specific interval from "summary" of Skills in Mathematics - Integral Calculus for JEE Main and Advanced by Amit M Agarwal
The concept of the definite integral is based on the idea that it represents the area under a curve on a specific interval. When we talk about the area under a curve, we are essentially looking at the region enclosed by the curve and the x-axis within a given interval. This region can be positive, negative, or zero, depending on the nature of the curve and the interval in question. To understand this concept better, let's consider a simple example. Suppose we have a curve defined by a function f(x) on the interval [a, b]. The definite integral of f(x) from a to b, denoted by ∫[a, b] f(x) dx, gives us the net area between the curve and the x-axis over the interval [a, b]. This net area takes into account the portions above and below the x-axis, with appropriate signs. It is important to note that the definite integral can be use...
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