A scientist is studying the potential of a chemical reaction, modeled by the equation
V=kt+12 V = k^t + 12 V=kt+12where kkk is a constant such that k>1k > 1k>1 and ttt is time. Sketch the graph of VVV against ttt.
On your sketch, show:
| ttt | 0 | 0.5 | 1 | 1.5 | 2 |
|---|---|---|---|---|---|
| R(t)R(t)R(t) | -3 | -2.2679 | -1 | 1.1962 | 5 |
The table shows corresponding values of time ttt and the rate of airflow R(t)R(t)R(t) in a ventilation shaft, where
R(t)=3t−4 R(t) = 3^t - 4 R(t)=3t−4Using the trapezium rule with all the values of R(t)R(t)R(t) in the given table, obtain an estimate for
∫02(3t−4) dt \int_{0}^{2} (3^t - 4) \, dt ∫02(3t−4)dtgiving your answer to 2 decimal places.
Using your answer to part (b) and making your method clear, estimate
(i)
∫02(3t+2) dt \int_{0}^{2} (3^t + 2) \, dt ∫02(3t+2)dt(ii)
∫02(3t+1−12) dt \int_{0}^{2} (3^{t+1} - 12) \, dt ∫02(3t+1−12)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.
