Chapter 7 Review #3 One more practice problem for AP Calculus AB – Chapter 7 1. Let f and g be the functions given by f ( x ) = − x 2 + 6 and g ( x ) = x 2 − 2 x + 2 . The graphs of f and g are shown in the figure below.

a) Find the area of the shaded region enclosed by the graphs of f and g.

b) Find the volume of the solid with the shaded region enclosed by the graphs of f and g as its base and equilateral triangle cross-sections perpendicular to the x –axis.

c) Find the length of the arc of f (x) between the two points where it intersects the graph of g (x).

d) Find the volume of the solid created by revolving the shaded region about the x – axis.

Chapter 7 Review #3 e) Find the volume of the solid when the area between f (x) and g (x) and from x = 0 to x = 2 is revolved around the y – axis.

f) Find the surface area of the solid when f (x) from x = 0 to x = 2 is revolved around the x – axis.