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.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, 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.
