The area between two curves is the total space enclosed by the two curves on a graph. It can be calculated by finding the definite integral of the difference between the two curves.
The variable to integrate with, x or y, depends on the orientation of the curves. If the curves are parallel to the x-axis, it is easier to integrate with x. If the curves are parallel to the y-axis, it is easier to integrate with y.
Yes, it is possible to integrate with both x and y. This is known as double integration and is used when the area between two curves is not easily represented by a single integral.
The integral for finding the area between two curves is set up by taking the integral of the difference between the two curves, with the limits of integration being the points of intersection between the curves.
Finding the area between two curves is important in many applications, such as calculating the volume of a solid or determining the work done by a moving object. It also helps in understanding the relationship between two functions and their behavior on a graph.