Matematikk - PreCalculus - Integrasjon 01 |
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The study of the relation between derivation and integration as 'opposite' operations. Predefined function y = 0.2x^2. Two points a and x are shown on the x-axis. The checkbox 'F(x)' shows the gray colored integration area. The values of the x-coordinates of the points a og x can be written in the datafield 'a' og 'x'. v Mark the checbox 'dF' to visualize an additional small area. Use the scrollbar to decrease the dF-area. Notice how the value of dF/dx approaches the value f of the integrand. Mark the checkbox 'Move Origin' to move the origin. A new function expression can be written in the datafield 'y'. The new graph is drawn immediately. The pushbutton 'Compute' has to used to compute the new correct area. - y = : The function expression (default 0.2x2) - a = : The x-value of the lower integration limit - x = : The x-value of the upper integration limit - F(x) : Show the shaded area between y = f(x), x = a, x = x, y = 0 - ΔF : Show the small shaded area between y = f(x), x = x, x = x + Δx, y = 0 - Formula1 : Show the formula of the relation between differentiation and integration - Formula2 : Same as Formula1, but in a more compact form - Move Origin : Move the origin - Scrollbar : Change Δx and therefore the width of ΔF - Reset : Reset the application |