Calculus

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)=(1/2)sin((2pi*t)/5) has often been used to model the rate of air flow into the lungs. Use this model to find the volume (in liters) of inhaled air in the lungs at time t.

This was my answer, but it's wrong...
-(5/(4pi))(cos((2pi*((5(t))/2))/5))+(5/(4pi))(cos((2pi*(0)/5)))

Use wolframalpha website, it helps!

Thank you for your time!

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  1. it says that
    (1/2)sin (2π/5)t is the rate of air flow
    then the volume would be the integral of the above

    V = (-5/(4π) cos(2πt/5) + c , where c is a constant

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