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Natural Science Department – Duy Tan University. FUBINI’S TH. (TRIPLE INTEGRALS). Lecturer: Ho Xuan Binh. FUBINI’S TH. (TRIPLE INTEGRALS). Natural Science Department – Duy Tan University. If f is continuous on the rectangular box B = [ a , b ] x [ c , d ] x [ r , s ], then.
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Natural Science Department – Duy Tan University FUBINI’S TH. (TRIPLE INTEGRALS) Lecturer: Ho Xuan Binh Da Nang-06/2015
FUBINI’S TH. (TRIPLE INTEGRALS) Natural Science Department – Duy Tan University If f is continuous on the rectangular box B = [a, b] x [c, d] x [r, s], then
FUBINI’S TH. (TRIPLE INTEGRALS) . Natural Science Department – Duy Tan University • The iterated integral on the right side of Fubini’s Theorem means that we integrate in the following order: • With respect to x (keeping y and z fixed) • With respect to y (keeping z fixed) • With respect to z
FUBINI’S TH. (TRIPLE INTEGRALS) Natural Science Department – Duy Tan University • There are five other possible orders in which we can integrate, all of which give the same value. • For instance, if we integrate with respect to y, then z, and then x, we have:
Example Natural Science Department – Duy Tan University Evaluate the triple integral where B is the rectangular box
