Answer the given questions related to the indicated examples of this section.

In Example 4, if you use only the data from the south end of (in km) 0, 3.00, 6.00, 9.00, 12.0, and 15.0, would you choose the trapezoidal rule or Simpson’s rule to calculate the area? Explain. Do not calculate the area for these data.

Data from Example 4

From an aerial photograph, a cartographer determines the widths of Easter Island (in the Pacific Ocean) at 1.50-km intervals as shown in Fig. 2.104. The widths found are as follows:

Since there are ten intervals, Simpson’s rule may be used. From the table, we have the following values: y₀ = 0, y₁ = 4.8, y₂ = 5.7,. . . ,  y₉ = 8.8, y₁₀ = 3.1, and h = 1.5. Using Simpson’s rule, the cartographer would approximate the area of Easter Island as follows:

Distance from South End (km) Width (km) 0 0 1.50 3.00 4.8 5.7 10.5 4.50 6.00 7.50 15.2 18.5 9.00 10.5 12.0 13.5 15.0 17.9 11.3 8.8 3.1 18.8