The rate of fuel consumption RRR of a prototype engine, in litres per hour, is modelled by the equation
R(t)=244t+tt R(t) = \frac{24}{4t + t\sqrt{t}} R(t)=4t+tt24where t≥1t \ge 1t≥1 is the time in hours since the engine was started. Use algebraic integration and the substitution u=tu = \sqrt{t}u=t to find the total fuel consumed between t=4t = 4t=4 and t=16t = 16t=16 hours. Write your answer in the form 12ln(ab)12 \ln \left( \frac{a}{b} \right)12ln(ba), where aaa and bbb are integers to be found. (Solutions relying entirely on calculator technology are not acceptable.)
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.
