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Applications of the
Integral Workshop




                Cal. Lab
(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
(2)   The object is farthest from the starting point at t =


                                             (a) 2       (b) 5    (c) 6


                                             (d) 8        (e) 9
(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
AP Calculus Slides February 29, 2008
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.
(a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.
(a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.
AP Calculus Slides February 29, 2008
AP Calculus Slides February 29, 2008
AP Calculus Slides February 29, 2008
AP Calculus Slides February 29, 2008
AP Calculus Slides February 29, 2008
AP Calculus Slides February 29, 2008
These are the answers, although they are not
    necessarily in the correct order. ;-)

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AP Calculus Slides February 29, 2008

  • 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. ;-)