The table below records the rate of a chemical reaction, R(t)R(t)R(t), in mol dm−3^{-3}−3 s−1^{-1}−1, at various times ttt seconds after initiation. The values of R(t)R(t)R(t) are rounded to 3 decimal places.
| ttt | 0.0 | 0.5 | 1.0 | 1.5 | 2.0 |
|---|---|---|---|---|---|
| R(t)R(t)R(t) | 0.420 | 1.258 | 2.115 | 1.643 | 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 change in concentration, given by
∫02R(t) dt \int_{0}^{2} R(t) \, dt ∫02R(t)dtgiving your answer to 2 decimal places.
Use your answer to part (a) to estimate (i)
[∫02(R(t)+5) dt [\int_{0}^{2} (R(t) + 5) \, dt [∫02(R(t)+5)dt(ii)
[∫13R(t−1) dt [\int_{1}^{3} R(t-1) \, dt [∫13R(t−1)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.
