Chapter 14.2, Problem 46E

Oil Production in Mexico: Pemex The rate of crude oil production from 2009 to 2013 by Pemex, Mexico’s national oil company, can be approximated by

$q\left(t\right)=6.2t^2-146t+1,910\text{ million barrels per year }\left(9\le t\le 13\right),$

Where t is time in years since that start of 2000. During that time, Mexico exported crude oil to the United States at a rate of ¹⁴

$r\left(t\right)=-14t^2+292t-1,100\text{ million barrels per year }\left(9\le t\le 13\right),$

Compute the area shown in the graph, and interpret the answer.

Year since 2000