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 [b]y = f(x) between x = a and x = b[/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.[br][br]Area Under a CurveCalculating the area under a curve. [u][b]Definite Integrals[/b][/u]So far when integrating, there has always been a constant term left. For this reason, such integrals are known as indefinite integrals. With definite integrals, we integrate a function between 2 points, and so we can find the precise value of the integral and there is no need for any unknown constant terms [the constant cancels out].[img]https://revisionworld.com/sites/revisionworld.com/files/imce/int3.gif[/img][u][b]The Area Under a Curve[/b][/u]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.[img]https://revisionworld.com/sites/revisionworld.com/files/imce/integration1.gif[/img]Areas under the x-axis will come out negative and areas above the x-axis will be positive. This means that you have to be careful when finding an area that is partly above and partly below the x-axis.[img]https://revisionworld.com/sites/revisionworld.com/files/imce/integration2.gif[/img]You may also be asked to find the area between the curve and the y-axis. To do this, integrate with respect to y.[i][b]Example[/b][/i]Find the area bounded by the lines y = 0, y = 1 and y = x2.[img]https://revisionworld.com/sites/revisionworld.com/files/imce/volume4.GIF[/img]