I.11.19 Triple integrals

\( \underline{\text { condition: }} \) Write the integral \[ \iiiint_{V} f(x, y, z) d x d y d z \] as an iterated integral, where \( V=\left\{(x, y, z): 0 \leq z \leq 4-x, y^{2} \leq 2 x+2\right\} \). The choice of which system and the order of recording is made from consideration of the region \(V\).