a Double Intergral of a function f(x,y) in the bounded region D is the sum of the products of the function f(xi,yi) with the area of the largest partitioned rectangle of the region D as the area of the largest partitioned rectangle goes to zero.

a Triple intergral of a function f(x,y,z) in the bounded region D is the sum of the products of the function f(xi,yi,zi) with the volume of the largest partitioned rectangle of the region D as the volume of the largest partitioned rectangle goes to zero.

2. Well, in your second definition, for the triple integral, you should say "rectangular prism" instead of rectangle, in order to correspond to the 3 dimensions. I'd say you were pretty close. You might want to say something about how the xi and yi and zi are chosen.

3. Originally Posted by Ackbeet
Well, in your second definition, for the triple integral, you should say "rectangular prism" instead of rectangle, in order to correspond to the 3 dimensions. I'd say you were pretty close. You might want to say something about how the xi and yi and zi are chosen.
Thanks, so I assume my definition of the double intergral is correct and my modified definition of the tripple intergral should be the following:

a Triple intergral of a function f(x,y,z) in the bounded region D is the sum of the products of the function f(xi,yi,zi) with the volume of the largest partitioned rectangle prism of the region D as the volume of the largest partitioned rectangle goes to zero and the volume is the product of xi,yi,zi as i repersents the order of the prism as we have n number of prisms in the region.

4. Better. You can check your work here.