Workshop style review of applications of integrals.

1. Applications of the
Integral Workshop
Cal. Lab

2. (1) At what time does the object attain its maximum acceleration?
(a) 2 < t < 5
(b) 5 < t < 8
(c) t = 6
(d) t = 8
(e) 8 < t < 9

3. (2) The object is farthest from the starting point at t =
(a) 2 (b) 5 (c) 6
(d) 8 (e) 9

4. (3) At t = 8 the object was at position x = 10. At t = 5, the position was x =
(a) -5 (b) 5 (c) 7
(d) 13 (e) 15

6. Greater Boston can be approximated by a semicircle of radius 8 miles with its
centre on the coast. Moving away from the centre along a radius, the population
density is constant for the first mile. Beyond that, the density starts to decrease
according to the data given in the table, where ρ(r), thousands/mile2, is the
population density at a distance r miles from the centre.
(a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.
(b) Determine a possible formula for ρ(r). Use this formula to make another
estimate of the population.

7. (a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.

8. (a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.

15. These are the answers, although they are not
necessarily in the correct order. ;-)