## On the Review of Riemann’s Line and Double (Surface) Integrals

Published: 2020-02-05

Page: 1-13

Eziokwu, C. Emmanuel *

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

In this work on Riemann’s integral, we discuss the integral for real valued function defined and bounded on finite intervals and then also for unbounded functions in finite intervals. We also extended the notion of integrals in another dimension. The interval  is replaced by a curve in two dimensional plane described by a vector valued function  and the integrand is vector function  defined and unbounded in this curve. The resulting integral is called the line integral or a contour integral and is denoted by  or by some similar symbol where the dot purposely suggest an inner product of two vectors. The curve is called a path of integration.

Keywords: Double integrals, finite closed interval, line integral, paths, partition of a rectangle, piecewise smooth path, scalar function.

#### How to Cite

Emmanuel, E. C. (2020). On the Review of Riemann’s Line and Double (Surface) Integrals. Asian Research Journal of Current Science, 2(1), 1–13. Retrieved from https://globalpresshub.com/index.php/ARJOCS/article/view/803

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