Triple Integral Calculator Level 2 calculates triple integrals of large variety of functions, it is a product which can be found most useful by scientists, engineers, professors, and students. This calculator calculates definite triple integrals of real functions with three real variables. Numerical values are calculated with precision up to 15 digits.
The calculator does not make any symbolic integration and any analytical guessing. The algorithm is purely numerical.
All calculation results are reflected in History rich-text-box, which can be saved in file or printed.
Limitations:
* 3-day trial period
The license of this software is Free Trial Software, the price is $85.00, you can free download and get a free trial.
The term “integral” can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing infinitesimal pieces to find the content of a continuous region. Other uses of “integral” include values that always take on integer values (e.g., integral embedding, integral graph), mathematical objects for which integers form basic examples (e.g., integral domain), and particular values of an equation (e.g., integral curve),
In calculus, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive. The process of computing an integral is called integration (a more archaic term for integration is quadrature), and the approximate computation of an integral is termed numerical integration.
Earlier in this chapter we showed how to convert a double integral in rectangular coordinates into a double integral in polar coordinates in order to deal more conveniently with problems involving circular symmetry. A similar situation occurs with triple integrals, but here we need to distinguish between cylindrical symmetry and spherical symmetry. In this section we convert triple integrals in rectangular coordinates into a triple integral in either cylindrical or spherical coordinates.
Also recall the chapter prelude, which showed the opera house l’Hemisphèric in Valencia, Spain. It has four sections with one of the sections being a theater in a five-story-high sphere (ball) under an oval roof as long as a football field. Inside is an IMAX screen that changes the sphere into a planetarium with a sky full of 9000 twinkling stars. Using triple integrals in spherical coordinates, we can find the volumes of different geometric shapes like these.