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.)
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.