Triple integral with dependent parameters.

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?

[David Goodmanson]

Hi Rohit, what do the functions look like? Hard to say much otherwise.

[Torsten]

Formally,

\left(\int_0^t g(x,t)dt\right

does not make sense because you cannot use t simultaneously as integration variable and upper bound for the integral.

What do you mean here ?

Best wishes

Torsten.