Definition (Definite Integral): Let be continuous on the closed interval

Finding Area between TwoCurves

Slicing, Approximating and Integrating with Respect to the X-Axis
Consider two curves defined by the two functions continuous on the closed interval We want to compute the area of the region between these two curves from to .

Let be a partition of In this way, we slice the region into  subregions. Let denote the the area of the subregion. We then approximate by the rectangular area where is any sample point in Thus, Intuitively, we feel that as , these approximations become better. Therefore, we define , area of , by integrating over That is,

If we are given two curves defined by the two functions continuous on the closed interval then we employ the same process as above only with respect to the as shown in Figure 3 and Figure 4 below.