how can I solve this problem with triple integrations I have tried this but I don't get the true value
$\int_1^3\int_1^2\int_0^{x^2y^2}dzdydx$
Find the volume of the solid bounded by the planes $z = 0, x = 1, x = 3, y = 1, y = 2,$ and surface $z = x^2y^2$?
I only want the triple integration in cartesian coordinates
The integral you have set up is correct for the problem as you have written it. Its value is $\frac{182}{9}$.
Either you've made a mistake transcribing the problem, or the "true answer" is wrong.