Answer
a) $ \int_{0}^1 \int_{0}^{1} f(x,y) dy dx +\int_{1}^{e} \int_{\ln x}^{1} f(x,y) dy dx $
---
(b) $\int_{0}^{1} \int_{0}^{e^y} f(x,y) dx dy$
Work Step by Step
(a) The region $R$ for vertical cross-sections can be written as follows:
$\iint_{R} \space 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) The region $R$ for horizontal cross-sections can be written as follows:
So, $\iint_{R} \space dA= \int_{0}^{1} \int_{0}^{e^y} f(x,y) dx dy$
