order of integration การใช้

• We assume that f \ is well behaved and that we can reverse the order of integration.
• In some cases, the order of integration can be validly interchanged; in others it cannot.
• Substituting these expressions into the entropy integral, exchanging the order of integration and summation, and using the orthogonality of the cosines, the entropy may be written:
• The convolution formula can be derived by substituting the defining Mellin Barnes integral for one of the G-functions, reversing the order of integration, and evaluating the inner Mellin-transform integral.
• For some functions " f " straightforward integration is feasible, but where that is not true, the integral can sometimes be reduced to simpler form by changing the order of integration.
• Using Fubini's theorem which allows one to interchange the order of integration, as well as integration by parts ( in " t " for the first term and in " x " for the second term ) this equation becomes
• In calculus, interchange of the "'order of integration "'is a methodology that transforms iterated integrals ( or multiple integrals through the use of Fubini's theorem ) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed.