The purpose of finding the area between two functions is to calculate the enclosed area or region that is bounded by the two functions. This can be useful in various scientific and mathematical applications, such as determining the total volume of a shape or finding the probability of an event occurring.
To solve for the area between two functions, you first need to find the points of intersection between the two functions. Then, you can use the definite integral to calculate the area under the curve between these points. In this case, the definite integral would be ∫(x2 - (-x))dx, with the limits of integration being from 0 to 2.
The limits of integration in this problem (0 to 2) represent the x-values of the points of intersection between the two functions. These limits determine the range over which the definite integral will be evaluated, and therefore, the area that will be calculated.
One way to verify the solution for the area between two functions is to graph the functions and visually check if the calculated area matches the actual enclosed area. Additionally, you can also use numerical methods, such as the midpoint rule or trapezoidal rule, to approximate the area and compare it to the calculated value.
Yes, there are many real-world applications for finding the area between two functions. For example, in physics, this concept is used to calculate the work done by a variable force over a certain distance. In economics, it can be used to determine the total profit or loss for a company. It is also commonly used in engineering, biology, and other fields of science and mathematics.