the average value is the sum of all values divided by the time. So, that is
(∫[0,10] v(t) dt)/10
= 1/10 ∫[0,10] 5/4π[1−cos((2/5)πt)] dt = 5π/4
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation 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)=1/2sin(2pi t/5) has often been used to model the rate of air flow into the lungs. This can then be used to show that the volume of inhaled air in the lungs at time t is given by V(t)=5/4π[1−cos((2/5)πt)]liters. Use this to compute the average volume (in liters) of inhaled air in the lungs in one respiratory cycle.
4 answers
The bounds should be 0 to 5, I'm not sure where the 10 is coming from. Also, the answer of 5pi/4 is incorrect
you are correct. It should be 5, not 10. But that does not change the answer. Better double-check the answer key.
I think it would change the answer because doesn't the 1/10 become 1/5 if we correct the error? Sorry, I just really have no idea how this problem works or how to do it.
6 answers