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The base of a solid is the region enclosed by the graphs of $y=\sin (x)$ and $y=4-\sqrt{x}$, between $x=2$ and $x=7$.$\newline$Cross sections of the solid perpendicular to the $x$-axis are rectangles whose height is $2 x$.$\newline$Which one of the definite integrals gives the volume of the solid?$\newline$Choose $1$ answer:$\newline$(A) $\int_{2}^{7}\left[(4-\sqrt{x})^{2}-\sin ^{2}(x)\right] d x$$\newline$(B) $\int_{2}^{7}[\sin (x)+\sqrt{x}-4] \cdot 2 x d x$$\newline$(C) $\int_{2}^{7}\left[\sin ^{2}(x)-(4-\sqrt{x})^{2}\right] d x$$\newline$(D) $\int_{2}^{7}[4-\sqrt{x}-\sin (x)] \cdot 2 x d x$