From a school course it is known that finding of the areas of figures on the coordinate plane requires knowledge of such concept as integral. For its application for determination of the areas of curvilinear trapezoids - quite so these figures are also called - to know certain algorithms enough.
Instruction
1. To calculate the area of a figure, a limited parabola, represent it in the Cartesian system of coordinates. For the image of a parabola it is necessary to know at least three points, one has to be top. To find top coordinate on axis X, substitute the known data in a formula x=-b/2a, on axis Y substitute the received value of an argument in function. After that analyze the data of the schedule entering a statement of the problem. If the top is lower than axis X, then branches will be directed up if above — down. Other 2 points are coordinates of crossing with an axis OH. Shade the received figure. It will significantly facilitate the solution of this task.
2. After that define integration limits. Usually they are specified in a statement of the problem by means of variables an and b. Place these values in more true and lower parts of a symbol of integral respectively. After a symbol of integral enter value of function in a general view and multiply it by dx (for example, (x²) dx in a case with a parabola). Then calculate an antiderivative of value of function in a general view, having used the special table according to the reference given in the section "Additional Sources" then substitute limits of integration there and find a difference. The received difference will also be the area.
3. Also there is a possibility of calculation of integral and a program method. For this purpose follow the link which is in the section "Additional Sources" to the special mathematical website. Enter integral of f(x) where f(x) is record of function which schedule limits the area of a figure on the coordinate plane into the opened text field. After input press the button in the form of a symbol "equally". The opened page will represent the received figure and also will show the course of calculations of its area.