Answer:
Given R (t) = 60/(1+t²), ft
/min
To find the amount of air in ft³, during the first min,
R (t) = 60/(1+t²
at t=1min, R is the air amount in ft³/min
Take the integral, and evaluate over [0,1]
Integral Of R (t) = 60/(1+t²) = 60 tan⁻¹(t),
60(Tan⁻¹(1) - Tan⁻¹(0)) = 60(pi/2) = 30 π
Therefore, it means that in the first minute, 30π ft³ of air escaped.
