Rate of air flow into the lungs is .

Net change theorem: .

Integrate the above function from  to  find volume of inhaled air in the lungs at a time .

.

Consider .

Apply derivative on each side.

Substitute  and  in .

Replace  in above expression.

.

Volume of inhaled air in the lungs at a time  is .

Volume of inhaled air in the lungs at a time  is .