Jack, the pool owner in Example 6.2.7, decides to use Simpson’s rule to recalculate the surface area of his pool by making the following measurements across the pool in 6-ft intervals instead of the 4-ft intervals shown in Figure 6.6. What is the recalculated area?

Data from Example 6.2.7

Jack needs to know the area of his swimming pool to buy a pool cover, but this is difficult because of the pool’s irregular shape. Suppose Jack makes the measurements shown in Figure 6.6 at 4-ft intervals along the base of the pool (all measurements are in feet). How can he use the trapezoidal rule to estimate the area?

Figure 6.6

Measurement point x; Width (in feet) of the pool at x; 0 0 6 10 12 18 8 8 24 12 30 36 12 0