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Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 7 s. the maximum rate of air flow into the lungs is about 0.3 l/s. this explains, in part, why the function f(t) = 3 10 sin(2πt/7) has often been used to model the rate of air flow into the lungs. use this model to find the volume of inhaled air in the lungs at time t.

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shinmin
In this problem, volume is computed:

volume = ∫(flow rate)·dt 

.. = ∫[0, t] (3/10)*sin(2πt/7)·dt

= (3 / 10)*(7 /(2 π))*(-cos (2 π t/7)+1) 

= (-21 / (20 π))*(cos (2 π t /7) - 1)

Volume is equal to 21 sin^2 (pit/7) / 10pi is the inhaled air in the lungs at time t

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