Question

after exercising for a few minutes a person has a respiratory cycle for which the rate of air intake is
v=1.75sin(pit/2)
find the volume, in liters, of air inhaled during one cycle by integrating the function over the interval (0,2).

Answer 1

\[V = 1.75\int\limits_{0}^{2} \sin(\frac{\pi}{2} t) dt\]
use substitution.......
u = (pi/2)t
du = pi/2 dt
\[V = (1.75)(\frac{2}{\pi})\int\limits_{0}^{2} \sin (u) du\]
\[V = (1.75)(\frac{2}{\pi})\left[ -\cos(\frac{\pi}{2} t) \right]\]
then evaluate from 0 to 2