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 Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
