The area under a curve can be described using an integral because an integral is essentially a mathematical tool that allows us to calculate the area under a curve. An integral is a mathematical concept that is used to find the area between a curve and the x-axis.
The integral is defined as the limit of the sum of the areas of an infinite number of rectangles, each with an infinitely small width, that are used to approximate the area under the curve. By taking the limit of this sum as the width of the rectangles approaches zero, we can find the exact area under the curve.
The integral is represented by the symbol ∫ and is written as the integral of a function f(x) over an interval [a, b]. The integral of f(x) over [a, b] is denoted by ∫[a, b] f(x) dx. The integral of f(x) over [a, b] gives us the area between the curve of f(x) and the x-axis over the interval [a, b].
In summary, an integral is a mathematical tool that allows us to calculate the area under a curve. We can use an integral to find the exact area under the curve by taking the limit of the sum of the areas of an infinite number of rectangles, each with an infinitely small width, that are used to approximate the area under the curve.