How do you find the area enclosed by the curve and the X-axis?

The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive.

How do you find the area between two curves on Desmos?

Just use the x-value. Type the limits of integration. Refer to the first function as f(x) and the second as g(x) – Desmos will know what function you are referring to. So here, you can simply type (f(x)-g(x)) dx.

How do you find area bound between two curves?

In general, two graphs y=f(x) and y=g(x) may cross. Sometimes f(x) may be larger and sometimes g(x) may be larger. In order to find the area enclosed by the curves, we can find where f(x) is larger, and where g(x) is larger, and then take the appropriate integrals of f(x)−g(x) or g(x)−f(x) respectively.

How do you find the area above and below the x axis?

The area above and below the x axis and the area between two curves is found by integrating, then evaluating from the limits of integration. Integration is also used to solve differential equations. To calculate the area between a curve and the \\ (x\\)-axis we must evaluate using definite integrals.

How do you find the area between two curves?

Area between curves. Example 9.1.3 Find the area between f ( x) = − x 2 + 4 x and g ( x) = x 2 − 6 x + 5 over the interval 0 ≤ x ≤ 1; the curves are shown in figure 9.1.4. Generally we should interpret “area” in the usual sense, as a necessarily positive quantity. Since the two curves cross, we need to compute two areas and add them.

How do you find the area of a rectangle with negative height?

The height of a typical rectangle will still be f ( x i) − g ( x i), even if g ( x i) is negative. Thus the area is ∫ 1 2 − x 2 + 4 x + 1 − ( − x 3 + 7 x 2 − 10 x + 3) d x = ∫ 1 2 x 3 − 8 x 2 + 14 x − 2 d x. Figure 9.1.3.

Is there a natural region between the two parabolas?

Here we are not given a specific interval, so it must be the case that there is a “natural” region involved. Since the curves are both parabolas, the only reasonable interpretation is the region between the two intersection points, which we found in the previous example: 5 ± 15 2.