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Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.5 $\mathrm{L} / \mathrm{s}$ . This explains, in part, why the function $f(t)=\frac{1}{2} \sin (2 \pi t / 5)$ 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 $t$.

$\frac{5}{4 \pi}[1-\cos (2 \pi t / 5)]$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

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Baylor University

University of Michigan - Ann Arbor

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this question asked us to use the model to find the volume of inhaled air in the lungs at Time T. What we know is that we have sign of two pi ti over five. We know the integral of sine is negative co sign And this what's in parentheses remains the same. Then we know that we have one minus this and we know they've given us ex. The ex elation takes about five seconds on the maximum rate of flow. Is your 50.5 which we know we can then right? One fourth times five. Given five seconds. This gives us five over for pie. We have five over for pie and then we have parentheses. This that is in

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