Question

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhaustion takes about 5 seconds.

The maximum rate of air flow into the lungs is about 0.5 L/s. This explains, in part, why the function f(t)={sin[(2pi*t)/5]}/2 has often been used to model the rate of air flow into the lungs. Use this model to find hte volume of inhaled air in the lungs at time t.

Answer 1

If f(t) is the flow rate in liters per second, integrating w.r.t. t should give you the volume function.

Answer 2

Solving for the integral I get:
\[\frac{ -5 }{ 4\pi }\ \cos (\frac{ 2\pi*t }{ 5 }) + C\]
But I don't know what to do with the other information....

Answer 3

I don't think there's much else to do. You could set up an initial boundary condition to find C by stating that volume =0 at time=0 . . .

Answer 4

Is the first part of the problem telling me that the definite integral from 0 to 5 seconds is 5 L/s?

Answer 5

No, those are the parameters used to develop the sine function model.

Answer 6

The full cycle in 5s is where the 2pi/5 comes from, and the 0.5l/s is the amplitude of the wave.