A gas flow system has a net rate of production R(t)R(t)R(t) given by R(t)=t4t+9R(t) = t\sqrt{4t+9}R(t)=t4t+9 in m3h−1\text{m}^3\text{h}^{-1}m3h−1, where t t\,t is time in hours.
Use integration by substitution to show that the net volume of gas produced during the interval −2.25≤t≤4-2.25 \le t \le 4−2.25≤t≤4, given by
V=∫−2.254t4t+9 dt V = \int_{-2.25}^{4} t\sqrt{4t+9} \, dt V=∫−2.254t4t+9dtis exactly 31.25 m3.
Fully justify your answer.
