# Area under the curve

This area can be obtained from a definite integral formula. The definite integral is useful in finding the area between the x-axis and the curve graph, between the two x-values. Such an area is referred to as area under a curve despite being below or above the x-axis. In this case, the formula Y= F(x) gives a result that is positive for the graphs that are positioned above the x-axis, and a result that is negative for the graphs that are positioned below the x-axis. In the case where the graph of y=f(x) appears being partly below the x-axis, the obtained area would e the net area. This is the difference between the area above the axis and the area below the axis.
Whenever the graph line is under the x-axis, the definite integral would be negative as shown in graph 2. The Y value for a graph below the x-axis is negative hence giving a negative value of ydx. It therefore shows that when an integral is negative, the area would certainly be below the x-axis.
In other cases, a section of the graph could be above the x-axis and another section below the x-axis. This situation calls for the calculation of several integrals. After getting the area of each section, the total area may be found by getting the sum of the sections.
From the sketch of the graph the y values are negative for -1 &lt. x &lt. 9, and positive for 0 &lt. x &lt. 2. I will calculate the area in two sections (A and B). The next step would be integrating the function, then substituting the limits one by one, and subtracting answers from the one above. This would be given as.
The second step would be integrating the function, then substituting the limits one by one, and subtracting answers from the one above (Donna, 2008). The function f(x) lying between 3 and -2 are the boundaries of different area segments. At x=-1 and x=2, zero can be seen hence the three different areas should be found. I will give the area the names: A1. A2, and A3