ap-calculus-ab 2001 Q1

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

Let $R$ and $S$ be the regions in the first quadrant shown in the figure above. The region $R$ is bounded by the $x$-axis and the graphs of $y = 2 - x^{3}$ and $y = \tan x$. The region $S$ is bounded by the $y$-axis and the graphs of $y = 2 - x^{3}$ and $y = \tan x$.
(a) Find the area of $R$.
(b) Find the area of $S$.
(c) Find the volume of the solid generated when $S$ is revolved about the $x$-axis.

Let $R$ and $S$ be the regions in the first quadrant shown in the figure above. The region $R$ is bounded by the $x$-axis and the graphs of $y = 2 - x^{3}$ and $y = \tan x$. The region $S$ is bounded by the $y$-axis and the graphs of $y = 2 - x^{3}$ and $y = \tan x$.\\
(a) Find the area of $R$.\\
(b) Find the area of $S$.\\
(c) Find the volume of the solid generated when $S$ is revolved about the $x$-axis.

Paper Questions

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