For the computational sake of integration, how would we integrate something such as $ \int x^2z^2 \space dz$ if we had that $ z^2=x^2+y^2$ and that $ 0 \le z \le 1$ were equations defining a cone in $ \mathbb R^3$ , where $ x$ and $ y$ are any points satisfying the equation.
I am getting confused with what happens when the variables in the integral are dependent on each other. If $ z$ was solely dependent on $ x$ then we could just substitute in for $ x$ in the integral and calculate it but because we have another variable $ y$ , I am slightly confused with how to proceed with this or whether this makes any sense at all.
As an aside, would this computation have any physical meaning or relevant interpretation that is worth mentioning?
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