![]() ![]() The formula to find the area under the curve with respect to the x-axis is A = \(_a\int^b f(x).dx\)Īrea with respect to the y-axis: The area of the curve bounded by the curve x = f(y), the y-axis, across the lines y = a and y = b is given by the following below expression. The bounding values for the curve with respect to the x-axis are a and b respectively. The below figures presents the area enclosed by the curve and the x-axis. For all these cases we have the derived formula to find the area under the curve.Īrea with respect to the x-axis: Here we shall first look at the area enclosed by the curve y = f(x) and the x-axis. For special cases, the curve is below the axes, and partly below the axes. The area under the curve can be calculated with respect to the x-axis or y-axis. The area of the curve can be calculated with respect to the different axes, as the boundary for the given curve. For a curve having an equation y = f(x), and bounded by the x-axis and with limit values of a and b respectively, the formula for the area under the curve is A = \( _a\int^b f(x).dx\) To find the area under the curve by this method integration we need the equation of the curve, the knowledge of the bounding lines or axis, and the boundary limiting points. Method - III: This method makes use of the integration process to find the area under the curve. This method is an easy method to find the area under the curve, but it only provides an approximate value of the area under the curve. Further, the areas of these rectangles are added to get the area under the curve. Here the area under the curve is divided into a few rectangles. Method - II: This method also uses a similar procedure as the above to find the area under the curve. The formula for the total area under the curve is A = \(\lim_^nf(x).\delta x\). Here we limit the number of rectangles up to infinity. For a curve y = f(x), it is broken into numerous rectangles of width \(\delta x\). The summation of the area of these rectangles gives the area under the curve. ![]() Method - I: Here the area under the curve is broken down into the smallest possible rectangles. Here we shall look into the below three methods to find the area under the curve. Also, the method used to find the area under the curve depends on the need and the available data inputs, to find the area under the curve. The area under the curve can be computed using three methods. 1.ĭifferent Methods to Find Area Under The Curve Here we shall learn how to find the area under the curve with respect to the axis, to find the area between a curve and a line, and to find the area between two curves. The process of integration helps to solve the equation and find the required area.įor finding the areas of irregular plane surfaces the methods of antiderivatives are very helpful. ![]() Generally, we have formulas for finding the areas of regular figures such as square, rectangle, quadrilateral, polygon, circle, but there is no defined formula to find the area under the curve. The area under the curve can be found by knowing the equation of the curve, the boundaries of the curve, and the axis enclosing the curve. Area under the curve is calculated by different methods, of which the antiderivative method of finding the area is most popular. ![]()
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