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

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.

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