# 8.1  Area
# 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:=-0.128*x^3 + 1.728*x^2 - 5.376*x + 2.864;

                          3          2
              f := -.128 x  + 1.728 x  - 5.376 x + 2.864

> plot(f, x=-2..10);
> rt:=fsolve(f=0, x);

             rt := .6697777844, 3.631759112, 9.198463104

> -Int(f, x=rt[1]..rt[2]) + Int(f, x=rt[2]..rt[3]);

    3.631759112
   /
  |                    3          2
- |             -.128 x  + 1.728 x  - 5.376 x + 2.864 dx
  |
 /
   .6697777844

          9.198463104
         /
        |                    3          2
     +  |             -.128 x  + 1.728 x  - 5.376 x + 2.864 dx
        |
       /
         3.631759112

> value(");

                             25.05016802

# Example 2
> g:=0.08*x^3 - 0.84*x^2 + 1.44*x + 4.32;

                           3        2
                 g := .08 x  - .84 x  + 1.44 x + 4.32

> plot({f, g}, x=-2..10);
> rt:=fsolve(f=g, x);

             rt := -.1985269946, 4.251804404, 8.292876437

> Int(g-f, x=rt[1]..rt[2]) + Int(f-g, x=rt[2]..rt[3]); value(");

   4.251804404
  /
 |                   3          2
 |             .208 x  - 2.568 x  + 6.816 x + 1.456 dx
 |
/
  -.1985269946

          8.292876437
         /
        |                    3          2
     +  |             -.208 x  + 2.568 x  - 6.816 x - 1.456 dx
        |
       /
         4.251804404


                             33.95029006

>