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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
