Answer
a) $\int_0^9 \int_{0}^{\sqrt x} f(x,y) dy dx$
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(b) $\int_{0}^{3} \int_{y^2}^{9} f(x,y) dx dy$
Work Step by Step
(a) The region $R$ for vertical cross-sections can be written as follows:
$R=$ { $( x,y) | 0 \leq y \leq \sqrt x , 0 \leq x \leq 9$}
$\iint_{R} dA=\int_0^9 \int_{0}^{\sqrt x} f(x,y) dy dx$
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(b) The region $R$ for horizontal cross-sections can be written as follows:
$R=$ { $( x,y) | y^2 \leq x \leq 9 , 0 \leq y \leq 3$}
and $\iint_{R} dA=\int_{0}^{3} \int_{y^2}^{9} f(x,y) dx dy$
