Solve a double integral: symbolically or numerically?

Question

Martina 2016-6-24

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https://ww2.mathworks.cn/matlabcentral/answers/292210-solve-a-double-integral-symbolically-or-numerically

回答： Walter Roberson 2016-6-24

Hello, I am trying to solve this double integral symbolically as

    syms i j b c d 
    f = (1/(d*j*sqrt(2*pi)))*exp(-0.5*((j-(b*i+c))^(2))/(d*j)^(2))
    int(int(f,j,20,25),i,20,21)

with b,c,d unknown parameters. Unfortunately I did not get any solutions. Thus, is there a way to solve it or do I have to try it numerically? If so, is it possible to solve numerical integral by keeping some parameters unknown?

Thank you in advance!!

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Answer 1

Walter Roberson 2016-6-24

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It is not possible to do a numeric integration with unknown parameters.

You might be able to get one step closer by exchanging the order of integration, but it looks like there might not be any known closed form for the double integral, even if you substitute in specific numeric values. You are going to have to use numeric integration for the overall solution.