Optimization Problem with integral

**clodilsognatore** · 10-01-2014, 09:11 PM

Hi everybody. May be the question is easy but it's making me crazy! I need to calculate numerically an integral from 0 to alpha, and then to optimize alpha as it results as much closes to a number (for example 0,7) as it can be! so I got:

0,7=1+4*(D1(alpha)-1)/alpha

with: D1(alpha)=1/alpha*integral_{0}^{alpha} x/(exp(x)-1)

How could I solve this in vba? I know i can solve it optimizing, but the matter is the integal...

Thank you very much indeed.

**MrShorty** · 10-01-2014, 10:55 PM

Do you remember your Riemann sums from calculus (http://en.wikipedia.org/wiki/Riemann_sum )? If not, I'd start by refreshing your memory.
It seems that most users (here anyway) prefer a trapezoidal rule Riemann sum for computing numerical integrals. The code for the integral should be relatively simple:

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From there, to optimize alpha. I would put the function (including the integration part) inside of a VBA UDF. Then, put that UDF inside of a spreadsheet with alpha. Then call Solver and tell it to optimize or find the root of the function cell by changing the alpha cell.