ABSTRACT
Vector calculus deals with the differentiation and integration of vector functions. In vector integral calculus, this chapter explains line integral, surface integral, and volume integral. It plays an important role in differential geometry and the study of partial differential equations. It is useful in the study of rigid dynamics, fluid dynamics, heat transfer, electromagnetism, theory of relativity, etc. The line integral is a simple generalization of a definite integral. In a line integral, the integration is done along a curve in space. The line integral depends only on the start and end values of the scalar potential, not on the path of the curve. The surface integral over a curved surface is the generalization of a double integral over a plane region. The plane region is the orthogonal projection of the curved surface on one of the coordinate planes.
