Answer
$16 \ln (3)$
Work Step by Step
Given: $ f(x, y, z)=\dfrac{z}{x}$
The iterated triple integral can be calculated as:
$\iiint_{\mathcal{B}} f(x,y,z)d V = \iiint_{\mathcal{B}} \dfrac{z}{x} d V \\
=\int_{1}^{3} \int_{0}^{2} \int_{0}^{4} [\dfrac{z}{x}] \ dz dy \ dx \\
= \int_{1}^{3} \int_{0}^{2} [\dfrac{z^2}{2x}]_0^4 \ dy \ dx\\=\int_{1}^{3} \int_0^2 \dfrac{8}{x} \ dy \ dx \\=\int_1^3 [\dfrac{8y}{x}]_0^2 \ dx \\=\int_1^3 (\dfrac{16}{x}) \ dx \\=16 [\ln |x|]_1^3 \\=16 [\ln (3) -\ln (1)] \\=16 \ln (3)$
