11. Let $A$ be the region bounded above by the graph of $y=\sin(\pi x)$ and below by the graph of $y=x^3-4x$.

(A) $(2.1,0.8)$ falls into the region $A$.

(B) The area of $A$ can be represented by $\displaystyle \int_0^2[\sin(\pi x)-(x^3-4x)]\,dx$.

(C) The area of $A$ is equal to 4.

(D) The region $A$ is the base of a solid. For this solid, each cross section perpendicular to the $x$-axis is a square. The volume of this solid is equal to $\displaystyle \int_0^2[\sin(\pi x)-(x^3-4x)]^2\,dx$.

(E) The region $A$ models the surface of a small pond. At all points in $A$ at a distance $x$ from the $y$-axis, the depth of the water is given by $h(x)=3-x$. The volume of water in the pond is equal to $\displaystyle \int_0^2(3-x)[\sin(\pi x)-(x^3-4x)]\,dx$.