Question

What is the Area Function?

Answer 1

Hint: In order to find the Area Function, we need to know about Area. An Area is the space bounded by curves or some region. An area function would describe some function having an area for some region based on some variables. We can find the area inside the curves by doing a definite integral between points.

Complete step by step solution:
The Area function is basically a function that describes some area of a region based on some variables like the area between a line and a parabola etc.
We can find the area under the curves or between two points by doing a definite integral between two points.
For example- To find the area between the curve $y = f\left( x \right)$ between $x = a$ and $x = b$, we would simply integrate $y = f\left( x \right)$ with the limits a and b. We would get the area under the x-axis as negative and the area above the x-axis as positive.
We are taking Definite Integrals instead of indefinite integrals because, when integrating, there is always a constant term left. For this reason, this kind of integrals are known as indefinite integrals, they don’t have limits. But, with definite integrals, we are integrating a function between two points, and so we can find the precise value of the integral and there is no need for any unknown constant terms [the constant cancels out].

Note: When we differentiate a constant term it gives zero, and we know integration is the opposite of integration, so integrating the values will return the terms differentiated but the constant term will not return back, that’s why a constant is added after integrating in order to fulfil the terms. But definite integral limits are given and we don’t need any constant.