Answer
$$V = 3$$
Work Step by Step
$$\eqalign{
& {\text{The volume of the solid is given by}} \cr
& V = \int_{ - 2}^2 {\int_0^{\ln 4} {{e^{ - x}}dx} } dy \cr
& {\text{Integrating}} \cr
& V = - \int_{ - 2}^2 {\left[ {{e^{ - x}}} \right]_0^{\ln 4}} dy \cr
& {\text{Evaluate the limits}} \cr
& V = - \int_{ - 2}^2 {\left( {\frac{1}{4} - 1} \right)} dy \cr
& V = \frac{3}{4}\int_{ - 2}^2 {dy} \cr
& {\text{Integrating}} \cr
& V = \frac{3}{4}\left[ y \right]_{ - 2}^2 \cr
& V = \frac{3}{4}\left[ {2 - \left( { - 2} \right)} \right] \cr
& V = 3 \cr} $$
