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Example of Triple Integral in Cartesian Coordinates

Example of Triple Integral in Cartesian Coordinates
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2015-02-02 03:17
Solid GeometryCalculusIntegral
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This example demonstrates how to calculate a triple integral using the Cartesian coordinate system. Key mathematical concepts include triple integrals and Cartesian coordinates. The Surface command is used to construct the 3D shape, and Textfield objects are utilized to input the integral limits. Suitable for teaching multivariable calculus in university courses.

GeoGebra Commands & Parameters

  1. Surface(xmin, (u * ymin(xmin)) + ((1 - u) * ymax(xmin)), (v * zmin(xmin, (u * ymin(xmin)) + ((1 - u) * ymax(xmin)))) + ((1 - v) * zmax(xmin, (u * ymin(xmin)) + ((1 - u) * ymax(xmin)))), u, 0, 1, v, 0, 1) → left
  2. Surface(xmax, (u * ymin(xmax)) + ((1 - u) * ymax(xmax)), (v * zmin(xmax, (u * ymin(xmax)) + ((1 - u) * ymax(xmax)))) + ((1 - v) * zmax(xmax, (u * ymin(xmax)) + ((1 - u) * ymax(xmax)))), u, 0, 1, v, 0, 1) → right
  3. Textfield(xmin) → textfield1
  4. Textfield(xmax) → textfield2
  5. Textfield(ymin) → textfield3
  6. Textfield(ymax) → textfield4
  7. Textfield(zmin) → textfield5
  8. Textfield(zmax) → textfield6
  9. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)), (v / 3 * zmin((u / 3 * xmin) + ((1 - u / 3) * xmax), ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))) + ((1 - v / 3) * zmax((u / 3 * xmin) + ((1 - u / 3) * xmax), ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → front
  10. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax))), zmax((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → up
  11. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), ymax((u / 3 * xmin) + ((1 - u / 3) * xmax)), (v / 3 * zmin((u / 3 * xmin) + ((1 - u / 3) * xmax), ymax((u / 3 * xmin) + ((1 - u / 3) * xmax)))) + ((1 - v / 3) * zmax((u / 3 * xmin) + ((1 - u / 3) * xmax), ymax((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → back
  12. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax))), zmin((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → down

AI Drawing Prompt Reference

Draw a 3D shape illustrating triple integration in Cartesian coordinates, featuring left and right surfaces, and front, back, up, and down surfaces, with text boxes for integral limits, showcasing the calculation process and spatial geometric relationships of triple integrals.
The prompt above was compiled from the original drawing commands and is for reference only.