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Math Help - Please help me verify my definition of the Double and Triple Intergral

  1. #1
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    Please help me verify my definition of the Double and Triple Intergral

    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.
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    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.
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  4. #4
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    Better. You can check your work here.
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