A region between a parabola and an…

Name: ______________________ Date: ____________ A region between a parabola and an exponential curve (9 points)

Graph

Let

f(x) = 5 - x^2

and

g(x) = e^{x/2}

. Let

R

be the region enclosed by the graphs of

f

and

g

, as shown. The graphs intersect at

x = a

and

x = b

, where

a < b

. A graphing calculator is required; use radian mode.

(a) Find the area of $R$ . [2 points]
(b) Find the volume of the solid generated when $R$ is revolved about the horizontal line $y = -2$ . [3 points]
(c) 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 the solid. [2 points]
(d) Write, but do not evaluate, an integral expression for the volume of the solid generated when $R$ is revolved about the horizontal line $y = 6$ . [2 points]

The question