MAT 213 Lecture Notes - Lecture 22: Riemann Sum, Centroid
Document Summary
Provide a generalization to each of the key terms listed in this section. When it comes to de ning single integrals with functions (of one variable) and even with double integrals for functions (of 2 variables), then you can actually de ne triple integrals for function (of 3 variables). So, the following is a general case while f (a function) can be de ned while on a rectangular box: B = {(x, y, z) | a x b, c y d, r z s} Bijk = [xi 1, xi] [yi 1, yi] [zi 1, zi] Xk=1 f (x ijk, y ijk, z ijk) v. De nition f "s (a function"s) triple integral that"s over b (a box) is the following while its limit does exist: Xk=1 f (x ijk) v ijk, y ijk, z . One things to keep in note is that a triple integral always exist if f (the function) is actually continuous.
