ap-calculus-ab 2002 Q1

ap-calculus-ab · Usa · free-response_formB Volumes of Revolution Multi-Part Area-and-Volume Free Response

Let $R$ be the region bounded by the $y$-axis and the graphs of $y = \frac{x^3}{1+x^2}$ and $y = 4 - 2x$, as shown in the figure above.
(a) Find the area of $R$.
(b) Find the volume of the solid generated when $R$ is revolved about the $x$-axis.
(c) The region $R$ is the base of a solid. For this solid, each cross section perpendicular to the $x$-axis is a square. Find the volume of this solid.

Let $R$ be the region bounded by the $y$-axis and the graphs of $y = \frac{x^3}{1+x^2}$ and $y = 4 - 2x$, as shown in the figure above.\\
(a) Find the area of $R$.\\
(b) Find the volume of the solid generated when $R$ is revolved about the $x$-axis.\\
(c) The region $R$ is the base of a solid. For this solid, each cross section perpendicular to the $x$-axis is a square. Find the volume of this solid.

Paper Questions

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