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)dt864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.