Answer
a) $\int_{0}^1 \int_{0}^{1} f(x,y) dy dx$
(b) $\int_{0}^{1} \int_{0}^{e^y} f(x,y) dx dy$
Work Step by Step
(a) For vertical cross-sections, the region $R$ can be defined as:
$\iint_{R} dA=\iint_{R_1} dA+\iint_{R_1} dA$
$= \int_{0}^1 \int_{0}^{1} f(x,y) dy dx +\int_{1}^{e} \int_{\ln x}^{1} f(x,y) dy dx $
(b) For horizontal cross-sections, the region $R$ can be defined as:
$\iint_{R} dA= \int_{0}^{1} \int_{0}^{e^y} f(x,y) dx dy$
