Let $f ( x ) = 2 x ^ { 2 } - 6 x + 4$ and $g ( x ) = 4 \cos \left( \frac { 1 } { 4 } \pi x \right)$. Let $R$ be the region bounded by the graphs of $f$ and $g$, as shown in the figure above. (a) Find the area of $R$. (b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when $R$ is rotated about the horizontal line $y = 4$. (c) The region $R$ is the base of a solid. For this solid, each cross section perpendicular to the $x$-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.
Let $f ( x ) = 2 x ^ { 2 } - 6 x + 4$ and $g ( x ) = 4 \cos \left( \frac { 1 } { 4 } \pi x \right)$. Let $R$ be the region bounded by the graphs of $f$ and $g$, as shown in the figure above.
(a) Find the area of $R$.
(b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when $R$ is rotated about the horizontal line $y = 4$.
(c) The region $R$ is the base of a solid. For this solid, each cross section perpendicular to the $x$-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.