7.1 Integral as Net Change

I. Net Area net area bounded by f(x) and the x-axis from a to b equals the NET CHANGE OF THE PRODUCT OF f(x)dx OVER [a, b]. 2) This is also the net change of the product f(x)*dx over [a,b]

The units of the area under the curve is the product of the units of the two axes. The position of a particle whose velocity function is given by v(t) is (starting position + how far you travelled).

II. Examples EX 1: A particle moving along a horizontal line has velocity where t is given in minutes and s is given in feet. Find the particle’s position at t = 4 if s(0) = 5.

EX 2: Find the total distance travelled in example 1.

EX 3: The world use of copper is increasing at a rate give by EX 3: The world use of copper is increasing at a rate give by in millions of tons of copper from 2001 forward. (a) Find the total amount of copper used from the beginning of 2001 to the beginning of 2006

(b) Find the total amount used from the beginning of 2006 to the end of 2008:

EX 4: The density of cars (in cars per mile) on the highway approaching Disney World is where x = the distance in miles from the Disney entrance. Find the total number of cars on the 10 mile stretch.

EX 5: In 2005, the world’s yearly petroleum consumption rate was about 22 billion barrels per year and was growing at 5%. How many years after 2005 is the world’s estimated oil reserves of 900 billion barrels likely to last?