AP ?s Help Related to Integrals

1. The rate of change of the altitude of a hot-air balloon is given by r(t) = t^3-4t^2+6 on [1,8]. Which of the following expressions gives the change in altitude of the balloon during the time the altitude is decreasing? (work too please)

3.514 8 2.667 3.514 2.667

a) ∫ r(t) dt b) ∫ r(t)dt c) ∫ r(t)dt d) ∫ r'(t)dt e) ∫ r'(t)dt

1.572 0 0 1.372 0

2. The rate of consumption of cola in the United states is given by S(t)= Ce^kt, where S is measured in billions of gallons per year andf t is measured in years from the beginning of 1980.

a) The consumption rate doubles every 5 years and the consumption rate at the beginning of 1980 was 6 billion gallons per year (when t=0, S(t)= 6). Find C and k.

b) Find the average rate of consumption of cola over the 10 year time period beginning Janurary 1, 1983. Indicate units of measure.

7

c) Use the trapezoidal rule with n=4 to estimate: ∫ S(t)dt

5

7

d) Using correct units, explain the meaning of: ∫ S(t)dt in terms of cola consumption.

5

Thanks so much

Re: AP ?s Help Related to Integrals

What have you done in working these two problems? I know for a fact that both problems are calculator active.

Re: AP ?s Help Related to Integrals

yeah so i had gotten the first one in the time that i had posted this using my calculator... but for the second one...i found c and k...c i got to be 6 and k to be ln2/5....but i dont know how to do the second part...do you use the secant? or the integral theorem?

Re: AP ?s Help Related to Integrals

avg value of a function ...

$\displaystyle f_{avg} = \frac{1}{b-a} \int_a^b f(x) \, dx$