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 dtV = \int_{-2.25}^{4} t\sqrt{4t+9} \, dtV=∫−2.254t4t+9dt
is exactly 31.25 m3.
Fully justify your answer.
Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.