I am sure this is the last time i am bothering you steve for today! you are very helpful.

Question

1) I have to find the population density i which r is 0.2 apart and distance is 1.2km so there are total 7 values from 0 to 1.2 , i am taking right and left end-point approximations and taking average of them, still not getting right answer?
2) Breathing cycle takes about 5 seconds.Maximum rate of flow is 0.5/L. The function often use to model the rate of air flow is 0.5sin(2pi*t/5). And volume of air inhaled in the lungs at time is given by 5/4*pi [1-cos(2*pi*t/5)]L. Find average volume of inhaled air in the lungs in one respiratory cycle

Answer 1

the density will be the (average value of the population) divided by the area

just as we had to integrate the density times area to get total population

.

Remember that the average value of f(x) in the interval [a,b] is

∫[a,b] f(x) dx
------------------
    b-a