Answer
a) $\int_0^9 \int_{0}^{\sqrt x} f(x,y) dy dx$
(b) $\int_{0}^{3} \int_{y^2}^{9} f(x,y) dx dy$
Work Step by Step
(a) For vertical cross-sections, the region $R$ can be defined as:
$R=$ { $( x,y) | 0 \leq y \leq \sqrt x , 0 \leq x \leq 9$}
Hence, we have $\int_0^9 \int_{0}^{\sqrt x} f(x,y) dy dx$
(b) For horizontal cross-sections, the region $R$ can be defined as:
$R=$ { $( x,y) | y^2 \leq x \leq 9 , 0 \leq y \leq 3$}
Hence, we have $\int_{0}^{3} \int_{y^2}^{9} f(x,y) dx dy$
