2. 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.
3. (a) Using this data and a Riemann sum, estimate the total
population living in the 8 mile radius.
HOMEWORK
4. (a) Using this data and a Riemann sum, estimate the total
population living in the 8 mile radius.
HOMEWORK
5. 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.
(b) Determine a possible formula for ρ(r). Use this formula to make
another estimate of the population.
13. These are the correct answers,
although they are not necessarily
in the correct order. ;-)
14. Now let's practice what we've learned ...
Find the average value of ƒ on the given interval.
Find c such that ƒ = ƒ(c).
ave
Sketch the graph of ƒ and a rectangle whose area is the same as
the area under the graph of ƒ.
ƒ(x) = 2x, [0, 3]
15. Now let's practice what we've learned ...
Find the average value of ƒ on the given interval.
Find c such that ƒ = ƒ(c).
ave
Sketch the graph of ƒ and a rectangle whose area is the same as
the area under the graph of ƒ.
16. Consider the region P bounded by the
graph of the function ƒ between x=-8
and x=-5.
Set up, but do not evaluate, the integral
that represents the volume of the solid
generated by revolving P about:
(a) the y-axis. (b) the line x=-10. (c) the line x=3.
17. Now let's practice what we've learned ...
Find the average value of ƒ on the given interval.
Find c such that ƒ = ƒ(c).
ave
Sketch the graph of ƒ and a rectangle whose area is the same as
the area under the graph of ƒ.
ƒ(x) = x 2 + 2x - 5, [-2, 2]