Definite integral window

Using GRAPES, polynomials of degree up to 8 can be integrated.
But other functions, we use the Definite integral window. The definite integral is calculated by the Simpson's method. Therefore, you are free to choose the number of partition.
GRAPES can display the integration area filled with your chosen colors and calculate the area of the enclosed by the graphs of two functions.

Open the Definite integral window

To open the Definite integral window, click the Definite integral button on the [Tool] palette.
Two vertical lines will be shown in the Graph area. These indicate the lower and the upper bounds of integration. The area of integration is shown in color.

The Function value window and the Definite integral window cannot be displayed at the same time.

Modification of the limit of integration

The following three ways of modification are available:

After clicking the Input area, input from calculator.
- Not only numerical values but also expressions can be input for a lower bound and for an upper bound.

Modify by dragging the vertical lines which indicate a lower bound and a upper bound.
- In this case, the lower and upper bounds cannot be given by expressions.
- The parts "sup" and "inf" at the top of the Definite integral window are the display buttons. While these buttons remain pressed, the vertical line will be hidden.

Display button

The parts "sup" and "inf" are the Display buttons. Clicking these buttons change the hide/show mode of the vertical lines which indicate the positions of the lower bound and the upper bound.

Coloring regions

The integration area of a function selected in "Show" group box will be identified by color in the Graph area.
The functions selected here change area under consideration.

Area of enclosed regions

GRAPES can calculate the area enclosed by the graphs of two functions (difference of two functions) selected from all defined functions.
By checking the function "subtracted" in the "Diff" group box, the integration values, that is differences, for all functions compared to this function will be shown.
You can select [0], then you will find the area enclosed between the graph and y = 0.

Using Definite integral to calculate area

The area under the graph of a function can be calculated integrating the absolute value of the function.
By clicking the button [Area] at the bottom part of the Definite integral window, you can calculate the desired area.

Modification of the number of partitions

When calculating by Simpson's method, the number of partitions can be modified, the range for the number of partitions must be even number between 2 to 200.