# 8.2 Volume # Art Belmonte, Summer 1996 # These are the shaded gray examples which appear in Section 8.1. # In-line plots have been removed to conserve disk space. # Example 1 > restart; f:=-x^2 + 5*x - 2; g:=x; plot({f, g}, x=0..4); 2 f := -x + 5 x - 2 g := x > a:=fsolve(f=g, x=0..1); b:=fsolve(f=g, x=3..4); a := .5857864376 b := 3.414213562 > Int(Pi * (f^2 - g^2), x=a..b); evalf("); 3.414213562 / | 2 2 2 | Pi ((-x + 5 x - 2) - x ) dx | / .5857864376 66.34705188 # Example 2 > Int(2*Pi*x * (f-g), x=a..b); evalf("); 3.414213562 / | 2 | 2 Pi x (-x + 4 x - 2) dx | / .5857864376 47.39075134 >