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)dt133 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.