Question

Air escapes from a balloon at a rate of 2 60 ( ) 1 R t t   3 ft / min , where t is measured in minutes. How much air (in 3 ft ) escapes during the first minute?

Answer 1

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.