ap-calculus-ab 2000 Q1

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

Let $R$ be the shaded region in the first quadrant enclosed by the graphs of $y = e ^ { - x ^ { 2 } } , y = 1 - \cos x$, and the $y$-axis, as shown in the figure above.
(a) Find the area of the region $R$.
(b) Find the volume of the solid generated when the region $R$ 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.

Correct limits in an integral in (a), (b), or (c).

Let $R$ be the shaded region in the first quadrant enclosed by the graphs of $y = e ^ { - x ^ { 2 } } , y = 1 - \cos x$, and the $y$-axis, as shown in the figure above.\\
(a) Find the area of the region $R$.\\
(b) Find the volume of the solid generated when the region $R$ 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

Q1 Q2 Q3 Q4 Q5 Q6