Abstract

## Role of Multiple Integral in Transform Calculus

Sanjay Jain1, Ashwini Nagpal2 and Kiran Bhateja3

1Department of Mathematics, S. P. C. Govt. P.G. College, Ajmer - 305 001, INDIA. 2Department of Mathematics, Seth G.L. Bihani S.D. P.G. College, Sriganganagar – 335001, INDIA. 3District Institute of Education and Training, Sri Muktsar Sahib – 152026 Research Scholar, Tantia University, Sri Ganganagar – 335002, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/690

### 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 hyper-volumes of multidimensional functions. The current paper highlights the role of multiple integral in mathematics.

Keywords :Multiple integration, Function, Variable, Integral, Domain.