In conventional 3D NURBS-based isogeometric analysis (IGA), it is required to generate a discretized 3D model from the imported CAD model. Since a CAD file only contains surface information of the 3D object, generation of 3D mesh and trivariate basis functions are required for the IGA. In CAD system, the Boolean difference operation, so-called "trimming" is frequently employed for creating complex objects. To directly utilize the trimming information into analysis, trimmed elements need to be defined and their integration schemes are also needed. In this paper, trimmed elements searching, classification, decomposition and integration rules are presented. In the process, seven types of generalized trimmed elements are defined. Since covering all possible 3D geometries is not possible, three out of seven types of trimmed elements formed by extrusion are treated. The decomposition rule of trimmed elements is introduced and curved tetrahedral cells are adopted to integrate the trimmed elements. For numerical integration of curved tetrahedral cells, 3D NEFEM-like integration scheme has been developed. For the demonstration of the usage of the developed elements, two numerical examples of trimmed volume are treated.