How can I solve this type of integration?

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I know how to determine either double integration and summation alone, but how could I solve both together as shown in pic.

Accepted Answer

Bjorn Gustavsson
Bjorn Gustavsson on 13 Aug 2021
This seems like a natural case for a for-loop. Something like this:
your_sum_of_integrals = 0;
for j1 = 1:100
your_sum_of_integrals = your_sum_of_integrals + (p-1)^2*integral2(@(theta,y) integrand_expr - etc;
A simple computational solution - there might be some clever way to figure out a closed-form solution of this, but this should be enough...
Bjorn Gustavsson
Bjorn Gustavsson on 24 Aug 2021
The way I understand your sum-of-integrals is that you integrate over y and θ and you sum such integrals over 100 values of p. That should leave you with one value for the sum without any independent variable it depends on. To make a graph you'd need some kind of variation to make it somewhat interesting, right? So what do you want to vary in this function? You could keep track of every term in the sums over p and j to make a 2-D surface/pseudo-color graph for example. But before I suggest something you'll have to explain what you want to plot...

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