Answer
a) $\int_0^2 \int_{1}^{e^x} f(x,y) dy dx$
b) $\int_{1}^{e^2} \int_{\ln (y)}^{2} f(x,y) dx dy$
Work Step by Step
(a) The region $R$ for vertical cross-sections can be written as follows:
$R=$ { $( x,y) | 1 \leq y \leq e^x , 0 \leq x \leq 2$}
so, $\iint_{R} dA=\int_0^2 \int_{1}^{e^x} f(x,y) dy dx$
(b) The region $R$ for horizontal cross-sections can be written as follows:
$R=$ { $( x,y) | \ln y \leq x \leq 2 , 1 \leq y \leq e^2$}
so, $\iint_{R} dA=\int_{1}^{e^2} \int_{\ln (y)}^{2} f(x,y) dx dy$
