Answer
a) $\int_0^{\pi/4} \int_{\tan x}^{1} f(x,y) dy dx$
b)$\int_{0}^{1} \int_{0}^{\tan^{-1} y} f(x,y) dx dy$
Work Step by Step
(a) For vertical cross-sections, the region $R$ can be defined as:
$R=$ { $( x,y) | \tan x \leq y \leq 1 , 0 \leq x \leq \dfrac{\pi}{4}$}
Hence, we have $\int_0^{\pi/4} \int_{\tan x}^{1} f(x,y) dy dx$
(b) For horizontal cross-sections, the region $R$ can be defined as:
$R=$ { $( x,y) | 0 \leq x \leq \tan^{-1} y , 0 \leq y \leq 1$}
Hence, we have $\int_{0}^{1} \int_{0}^{\tan^{-1} y} f(x,y) dx dy$
