More applications of integrals using a function defined symbolically or numerically as the problem stem.

1. The quot;Boston By
The Seaquot; Problem
Boston Harbor Dusk

6. Suppose the density of a circular oil slick on the surface of a body of water
kg/m2.
is given by
(a) Suppose that the slick extends from r = 0 to r = 1000 m.
Determine the mass of the oil slick to the nearest kg.

7. Suppose the density of a circular oil slick on the surface of a body of water
2.
is given by kg/m
(a) Suppose that the slick extends from r = 0 to r = 1000 m.
Determine the mass of the oil slick to the nearest kg. 4340
(b) What is the smallest radius that contains 75% of the oil slick’s mass?
(177.8)

8. Suppose the density of cars, in cars/km for the first 30 km along Main
Street during certain hours of the day can be modeled by
where x represents the number of kilometers from the corner of Portage
and Main.
(a) Write a function that gives the number of cars from Portage and
Main to a point x km along Main Street. Do not simplify.

9. Suppose the density of cars, in cars/km for the first 30 km along Main
Street during certain hours of the day can be modeled by
where x represents the number of kilometers from the corner of Portage
and Main.
(b) To the nearest car, how many cars are there on this 30 km
stretch of road?

10. 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.

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