A pharmaceutical researcher models the concentration of a therapeutic drug, CCC, in milligrams per litre (mg/L), present in a patient's bloodstream ttt hours after the initial dose using the function:
C(t)=26−2t+1,t≥0 C(t) = 2^{6 - \sqrt{2t+1}}, \quad t \ge 0 C(t)=26−2t+1,t≥0The table below shows corresponding values of ttt and C(t)C(t)C(t). The values of C(t)C(t)C(t) are given to 3 decimal places.
| ttt | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|
| C(t)C(t)C(t) | 8.000 | 5.258 | 3.673 | 2.671 | 2.000 |
Using the trapezium rule with all the values in the table:
obtain an estimate for the total drug exposure over the interval 4≤t≤124 \le t \le 124≤t≤12, given by ∫412C(t) dt\int_{4}^{12} C(t) \, dt∫412C(t)dt, giving your answer to 2 decimal places.
Using your answer to part (a) and making your method clear, estimate
(i) ∫41227−2t+1 dt\int_{4}^{12} 2^{7-\sqrt{2t+1}} \, dt∫41227−2t+1dt
(ii) ∫412(C(t)+5) dt\int_{4}^{12} (C(t) + 5) \, dt∫412(C(t)+5)dt
864 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.