57 Journal of Science and Technology UTHM On C Integral in the n-Dimensional Euclidean Space Tutut Herawan Faculty of Information Technology and Multimedia Universiti Tun Hussein Onn Malaysia Parit Raja, Batu Pahat 86400, Johor, Malaysia *Corresponding email: tututherawan@yahoo.com Abstract In this paper, we generalize C integral on real line to the n-dimensional Euclidean space. Further, we present the Cauchy criterion for C integrability, the relation between C and Henstock integrals. Finally, we prove that monotone and dominated convergence theorems for the C integral are still valid in the n-dimensional Euclidean space. Keywords: The n-dimensional Euclidean space; C integral; Cauchy criterion; Monotone and dominated convergence theorems. chap 5.indd 57 15/01/2010 9:04:52 AM