Chapter 7.CR, Problem 87CR

Oil Production The following table shows the amount of crude oil (in billions of barrels) produced in the United States in recent years. Source: U.S. Energy Information Administration.

Year	Crude Oil Produced
$2002$	$2.097$
$2003$	$2.060$
$2004$	$1.989$
$2005$	$1.893$
$2006$	$1.857$
$2007$	$1.853$
$2008$	$1.830$
$2009$	$1.954$
$2010$	$2.000$
$2011$	$2.063$
$2012$	$2.377$

In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above.

1. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation.
2. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter.
3. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting $t=0$ correspond to 2000. Then integrate this equation over the interval $\left[2.12\right]$ to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.