Wetzel

Math 140

4.4 – The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus –

Ex.:

1.)                                                

2.)  Find the area under the curve of  on [0, 2].

3.)                                                        4.) 

Average Value Theorem –

                        If  is integrable on the closed interval [a, b], then the average value of on the interval is

Ex.:

5.)  Find the average value of the function over the given interval

                     [1, 3]

6.)  The cost per unit of producing CD players over a two-year period is modeled by

            where t is the time in months.  Approximate the average cost per unit over the two-year period.

*7.)  The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model

where t is the time in seconds.  Approximate the average volume of air in the lungs during one cycle.

HW:  p.291  #5-37odd, 47, 49, 63