Matematikk - PreCalculus - Integrasjon 01 UiA Logo


[SimReal] [Library]
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

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