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The base of a solid is the region enclosed by the graphs of $y=2+\frac{x}{2}$ and $y=2^{\frac{x}{2}}$, between the $y$-axis and $x=4$.$\newline$Cross sections of the solid perpendicular to the $x$-axis are rectangles whose height is $4-x$.$\newline$Which one of the definite integrals gives the volume of the solid?$\newline$Choose $1$ answer:$\newline$(A) $\int_{0}^{4}\left[2^{\frac{x}{2}}-\frac{x}{2}-2\right](4-x) d x$$\newline$(B) $\int_{0}^{4}\left[2^{\frac{x}{2}}+\frac{x}{2}+2\right](4-x) d x$$\newline$(C) $\int_{0}^{4}\left[2+\frac{x}{2}-2^{\frac{x}{2}}\right](4-x) d x$$\newline$(D) $\int_{0}^{4}\left[2^{\frac{x}{2}}-\frac{x}{2}+2\right](4-x) d x$