Area between curves

1: Suppose your annual income is

I(t) = 63,000 + 2,000t (0 t 3)

dollars per year, where t represents the number of years since you began your job, while your annual expenses are

E(t) = 52,000 + 1,500t (0 t 3)

dollars per year. Find the area (in dollars) between the graphs of I(t) and E(t) for 0 t 3. $ ______________

2: The following models show the rate at which new members joined Facebook and MySpace in the period from 2005 to the middle of 2008.(t is time in years since the start of 2005.)

Facebook:	f(t)	=	12t2		20t	+	10 million members per year (0 t 3.5)
MySpace:	m(t)	=	10.5t2	+	25t	+	18.5 million members per year (0 t 3.5)

a: Use an integral to estimate how many more people joined that Internet site than joined its competitor during that period. (Round your answer to the nearest million.)

__________________ million members

b: To what area does the integral used in part (a) correspond?

The integral in part (a) corresponds to the area _____________the curve

y = f(t) and___________over the interval ________________, ________________

3: The rate of crude oil production from 2009 to 2013 by Pemex, Mexico's national oil company, can be approximated by

q(t) = 6.2t² 146t + 1,910 million barrels per year (9 t 13),

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

r(t) = 14t² + 292t 1,100 million barrels per year (9 t 13).

Compute the area shown in the graph. (Round your answer to the nearest whole number.)