A chemical engineer monitors the rate of a reaction, R(t)R(t)R(t), measured in mmol L−1^{-1}−1 min−1^{-1}−1, at regular intervals during the first 8 minutes of a process. The following table records the measured rate at various times t t\,t in minutes. The values of R(t)R(t)R(t) are rounded to 3 decimal places.
| ttt | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| R(t)R(t)R(t) | 0.450 | 1.282 | 2.914 | 1.845 | 0.312 |
Using the trapezium rule with all the values of R(t)R(t)R(t) in the given table, obtain an estimate for the total yield of the substance, given by
∫08R(t) dt \int_{0}^{8} R(t) \, dt ∫08R(t)dtgiving your answer to 2 decimal places.
Use your answer to part (a) to estimate (i)
[∫08(R(t)−0.2) dt [\int_{0}^{8} (R(t) - 0.2) \, dt [∫08(R(t)−0.2)dt(ii)
[∫311R(t−3) dt [\int_{3}^{11} R(t-3) \, dt [∫311R(t−3)dtPractise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (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.
