The rate of fuel consumption RRR of a prototype engine, in litres per hour, is modelled by the equation R(t)=244t+ttR(t) = \frac{24}{4t + t\sqrt{t}}R(t)=4t+tt24 where 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 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.