Answer
(a) $\int_{e^{-x}}^1 \int_{0}^{\ln 3} f(x,y) dy dx$
(b) $\int_{-\ln y}^{\ln 3} \int_{1/3}^{1} f(x,y) dx dy$
Work Step by Step
(a) The region $R$ for horizontal cross-sections can be written as follows:
$R=$ { $( x,y) | e^{-x} \leq y \leq 1 , 0 \leq x \leq \ln (3) $}
$\iint_{R} dA=\int_{e^{-x}}^1 \int_{0}^{\ln 3} f(x,y) dy dx$
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(b) The region $R$ for horizontal cross-sections can be written as follows:
$R=$ { $( x,y) | -\ln y \leq x \leq \ln 3 , \dfrac{1}{3} \leq y \leq 1$}
$\iint_{R} dA=\int_{-\ln y}^{\ln 3} \int_{1/3}^{1} f(x,y) dx dy$
