International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2017, Vol. 2, Issue 6, Part C

Multiple integration of a function


Author(s): Pramod Shinde and Dr. Ashwini Nagpal

Abstract: The multiple integral is a generalization of the definite integral to functions of more than one real variable, for example, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in R2 are called double integrals, and integrals of a function of three variables over a region of R3 are called triple integrals. Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. (The same volume can be obtained via the triple integral—the integral of a function in three variables—of the constant function f(x, y, z) = 1 over the above-mentioned region between the surface and the plane.) If there are more variables, a multiple integral will yield hypervolumes of multidimensional functions.

Pages: 155-158 | Views: 556 | Downloads: 22

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How to cite this article:
Pramod Shinde and Dr. Ashwini Nagpal. Multiple integration of a function. International Journal of Statistics and Applied Mathematics. 2017; 2(6): 155-158.
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