1. Da Nang-06/2015 Natural Science Department – Duy Tan University Lecturer: Ho Xuan Binh FUBINI’S TH. (TRIPLE INTEGRALS)

2. Natural Science Department – Duy Tan University If f is continuous on the rectangular box B = [a, b] x [c, d] x [r, s], then

3. 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: 1.With respect to x (keeping y and z fixed) 2.With respect to y (keeping z fixed) 3.With respect to z

4. 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:

5. Example Natural Science Department – Duy Tan University Evaluate the triple integral where B is the rectangular box

6. LOGO Thank you for your attention