I'm trying to figure out how to solve this definite integral:
$\int _0^z\left(x(l)+ \int_0^l\left(w(r)dr\right)\right)dl$
As you can see the $z$ is the range of integration (constant) and the inner integral is varying its integration range between $0$ and $l$, which is the outer integration variable.
Is it possible to apply Gauss Quadrature to approximate this definite integral having the generic functions $x(t)$ and $w(t)$ and the value of $z$ ?
EDIT: I would need to get an approximation of the integral above given the two generic functions and the integration limit. Considering that Gauss quadrature can be applied to a single function I would like to know if it is possible to use the tool to evaluate this double finite integral with the possibility to increase the precision using more weights.