According to a theorem partially proven by Ostrogadsky, this operation yields zero if a vector field is divergent free. The determinant of the Jacobian is used as a multiplicative factor when changing variables for this operation. One of these operations is equated to a line integral around a simple closed curve by Green's theorem. This operation can sometimes be more easily evaluated by transforming to polar, cylindrical or spherical coordinates. The order in which this operation is performed c
According to a theorem partially proven by Ostrogadsky, this operation yields zero if a vector field is divergent free. The determinant of the Jacobian is used as a multiplicative factor when changing variables for this operation. One of these operations is equated to a line integral around a simple closed curve by Green's theorem. This operation can sometimes be more easily evaluated by transforming to polar, cylindrical or spherical coordinates. The order in which this operation is performed can be changed as a consequence of Fubini's theorem. For 10 points, identify this operation that involves multiple Riemannian sums and can be used to find surface area or volume.
According to a theorem partially proven by Ostrogadsky, this operation yields zero if a vector field is divergent free.
multiple integrals [or double integrals; or triple integrals; or surface integrals; or flux integrals; or word forms of "integral", such as integration; prompt on integration]