|Matematikk - Multiple integraler|
Triple Integral - T02
Visualization of computing a triple integral.
The object enclosed by five planes:
x = 0, x = 2, y = 0, z = 0, z = 0 and z = y - 1.
The object has six corners (0,0,0) - (2,0,0) - (2,1,0) - (0,1,0), (3,0,3), (0,0,1) and (2,1,0).
The object can be turned around and viewed from different directions.
The application always starts by showing an infinitesimal volume element inside the object.
This volume element grows under the integration process to visualize what the integration means.
There are six ways the triple integration can be done dependent on the order of integration:
dxdydz - dxdzdy - dydxdz - dydzdx - dzdxdy - dzdydx
You can select among these six ways by the help of the six radiobuttons in the control window (default radiobutton is dzdydx).
The integration is done by the help of the three scrollbars in the middle of the control window.
These scrollbars are always arranged in 'right order' so they should be applied from the top to the bottom.
The scrollbar 'Move' moves the volume element illustrating the sum process in the integration.
Down to the left in the simulation window the formula with colored parts of integration is shown.