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Fred_KohlheppAnswer
23-Emerald I
February 21, 2024

Careful!

Simply summing is not the same as integration

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Fred_Kohlhepp23-Emerald I
23-Emerald I
February 21, 2024

Integration requires that you have a function defined over the entire range.  You've got q defined at discrete points.  You might try simple linear interpolation to define a function.

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    LucMeekes23-Emerald IV
    23-Emerald IV
    February 21, 2024

    It's always better to attach the Prime worksheet, and state which version of Prime you are using.

    Regarding the integration: You have a vector of values. Simply sum the vector values for the range that coincides with z going from 0 to DeltaL. You can use the summing operator for that.

     

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    Luc

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      Fred_Kohlhepp23-Emerald IAnswer
      23-Emerald I
      February 21, 2024

      Careful!

      Simply summing is not the same as integration

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        Werner_E
        Werner_E25-Diamond I
        25-Diamond I
        February 21, 2024
        @Fred_Kohlhepp wrote:

        Careful!

        Simply summing is not the same as integration

        Agreed on, but not the way you had shown it.

        To approximate the integral we must multiply the function values by the differences of the z-values.

        In the example you gave these differences are constant 1 in, so you have to multiply the H-sum by 1 in, not by the total 4 in.

        Furthermore you have to omit either the last or the first value in vector H to get the lower or upper rectangle sum.

        The mean of this sum is what you get using trapezoid "integration".

        Werner_E_0-1708554211627.png

         

        trapezoid is the very same as what you should get by using linear interpolation. Adding dummy values at the end we even can get Prime to give us the result for the integral over the interpolated function.

        Werner_E_1-1708554311634.png

         

         

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