We turn now to integrals over curved surfaces in space. They are analogous,in several ways, to integrals over curved paths. Both arise in scientific problems as ways to express the product of quantities that vary. The first surface integral we consider measures flux, the amount of fluid flowing through a surface. The integrand of a surface integral, like a path integral, can be either a scalar or a vector function: flux is the integral of a vector function, whereas area—another surface integral—is the integral of a scalar. Also, orientation matters, at least when the integrand is a vector function.
KeywordsDifferential Form Scalar Integral Oriented Surface Surface Patch Coordinate Change
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