Chapter 6.6, Problem 44E

Is evaluated in much the same way as a double iterated integral. We first evaluate the inside x-integral, treating y and z as constants Then we evaluate three middle y-integral, treating z as a constant. Finally we evaluate the outside z-integral Evaluate the following triple integrals.

${\displaystyle {\int }_0^2{\displaystyle {\int }_{2-y}^{6-2y}{\displaystyle {\int }_0^{\sqrt{4-y^2}}zdzdydx}}}$