Question

3. The graphs shows the rate at which U.S. oil was produced and imported between 1920 and 2005 in units of millions of barrels per day. The total amount of oil produced or imported would therefore be the area of the region under the corresponding curve. U.S. Oil Production and Imports Use a numerical method of your choice to estimate the total amount of oil produced in the U.S. between 10 1940 and 2000. Be careful with units; time is Production measured both in days and years in this problem. Imports 2000 1940 1960 1980 1920 Year Repsaueq

Answer 1

To estimate the amount of US oil produced between 1940 and 2000 by numerical integration

Use the midpoint rule to estimate the amount of US oil produced

Midpoint Rule:

f(x)da f(m1)Arf(m2)A f(mn)Ar

The midpoint from the graph are:

Year	1945	1955	1965	1975	1985	1995
No of barrels in milllios/day	4.5	6.2	7.5	9	9	6.5

As the number of intervals are n = 6,so the length of each interval $\Delta$x is expressed as

60 Ar20001940 10 6

Integration:

r2000 f(z)dr4.5 106.2 10 +7.5 10910 910+6.5 10 1940

4562 75+909065

=427

So the results is 427 * 10⁶ (millions per day)

As the number of days per year is 365

Total production = 427 * 10⁶ * 365 = 1.6 * 10¹¹

So the number of barrels of US oils produced is 1.6 * 10¹¹