| SimReal / Python / Matlab: Programming - Exercise - Mathematics - Integration | |
SimReal - Python - Matlab |
001. Integration Write an application so you can study the integration of a function by appoximating an area with rectangles. Let the function be given by: y = f(x) = -0.1x2 + 6 and integrate this function from x = - 7 to x = 5. Control the result by integrating by hand. |
SimReal - Python - Matlab |
002. Curve Length Write an application that compute the length of the curve of the function: y = f(x) = xcos(x) between the two points (-7,f(-7)) and (5,f(5)). Find the length by approximating the curve by smaller and smaller line segments. |
SimReal - Python - Matlab |
003. Area - Single integral - nquad Write an application that compute the area between the graph of the function y = 5-0.2(x-4)2, the x-axis and the two vertical lines x=1 and x=8. Use the integration-function nquad for single integral in the Python library scipy. |
SimReal - Python - Matlab |
004. Area - Double integral - nquad Same as exercise 003, except that now with the integration-function nquad for double integral: Write an application that compute the area between the graph of the function y = 5-0.2(x-4)2, the x-axis and the two vertical lines x=1 and x=8. Use the integration-function nquad for double integral in the Python library scipy. |
SimReal - Python - Matlab |
005. Area / Mass / Center of Mass - Double integral - nquad Write an application that compute the area, the mass and the center of mass for the plane area between the graph of the function y = 5-0.2(x-4)2, the x-axis and the two vertical lines x=1 and x=8. . The mass density of the area is xy2. Use the integration-function nquad for double integral in the Python library scipy. |
SimReal - Python - Matlab |
006. Volume - Triple integral - nquad Write an application that compute the volume of the objectin 3D between the following planes: x = 0 y = 1 z = 0 z = y - x Use the integration-function nquad for triple integral in the Python library scipy. |
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SimReal - Python - Matlab |
007. Volume / Mass / Center of Mass - Triple integral - nquad Write an application that compute the volume, the mass and the center of mass for the object in 3D between the following planes: x = 0 y = 1 z = 0 z = y - x Use the integration-function nquad for triple integral in the Python library scipy. |
SimReal - Python - JSXGraph |
008. Integral Multiple Programming exercises with single, double and triple integrals. Computing curve integral, length, area, volume and center of mass. |
SimReal - Python - Matlab |
009. Integration - Symbolic Programming the symbolic integration of the function: f(x) = x·cos(x). Draw the graph of both the function f and it's integral function. |
