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)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.