Mastering Area Calculation: A Guide To Finding Area Between Two Curves Using Integration

Area between two curves

integral of (top curve-bottom curve) from a to b(with respect to x)integral of (right curve – left curve) from a to b(with respect to y)

The area between two curves is the total region that is enclosed by two curves on a graphical representation. In order to find the area between two curves, we must first identify the specific region we are interested in, and then determine the bounds of integration necessary to calculate the area.

To find the area between two curves, we typically use integration. We integrate the area of the individual slices which are perpendicular to the x-axis or y-axis depending on which axis the slices are perpendicular to. Once we determine the boundaries of the region, we need to set up the integral that can be calculated to obtain the area.

We can find the area between two curves either by integrating with respect to x or y. If we integrate with respect to x, we will be summing the areas of the slices that are perpendicular to the x-axis. If we integrate with respect to y, we will be summing the areas of the slices that are perpendicular to the y-axis.

For example, if we consider two curves f(x) and g(x), and we want to find the area between them from x = a to x = b, we write the integral:

Area = ∫[a,b] [f(x) – g(x)]dx

Similarly, if we consider two curves f(y) and g(y), and we want to find the area between them from y = c to y = d, we write the integral :

Area = ∫[c,d] [f(y) – g(y)]dy

We integrate the equations with the specific limits of the region in consideration. Once the integral is calculated, it will give us the area between the two curves.

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