Triple integral with dependent parameters.

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Rohit Goswami 2017-11-25

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https://ww2.mathworks.cn/matlabcentral/answers/369239-triple-integral-with-dependent-parameters

编辑： Torsten 2017-11-27

The form of my problem is as follows:

$\Psi=C\int_{-\inf}^\inf\int_{-\inf}^\inf\left(f(x,y)\times \left(\int_0^t g(x,t)dt\right)dxdy\right)$

I have already attempted numerical solutions using Matlab's ```integrate3```, without success. However ```integrate3``` is meant for problems of the form:

$\Psi=\int_a^b\int_c^d\int_e^f f(x,y,z)dxdydz$

Similarly, attempts made with scipy's integration toolkit have also not borne fruit.

I have attempted to first calculate $\int_0^tg(x,t)$ at discrete $x$ values and then place it in $\Psi$ but for rather obvious reasons that does not work either.

Additionally, $g(x,t)$ cannot be factored in the form of $h(x)\times i(t)$, which might have allowed for a by parts solution which might be integrated symbolically (for x) and numerically for t.

Also $\int_0^t\int_{-\inf}^{\inf} g(x,t)$ has singularities at multiple points.

Is there a cannonical way of solving this?