An environmental biologist monitors the growth rate of a rare fern species. The rate of change of the leaf surface area, RRR (in cm2\text{cm}^2cm2 per week), is modeled by the function R(t)=ln(t+4)R(t) = \ln(t + 4)R(t)=ln(t+4), where ttt is the time in weeks after the initial measurement. The table below shows the observed values for the first 5 weeks.
| ttt | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| R(t)R(t)R(t) | ln4\ln 4ln4 | ln5\ln 5ln5 | ln6\ln 6ln6 | ln7\ln 7ln7 | ln8\ln 8ln8 | ln9\ln 9ln9 |
Using the trapezium rule with all the values in the table, show that the total change in surface area over the 5-week period can be approximated as
∫05ln(t+4) dt≈lnk \int_{0}^{5} \ln(t + 4) \, dt \approx \ln k ∫05ln(t+4)dt≈lnkwhere kkk is an integer to be found.
Determine the value of www that satisfies the equation
2log4(w+3)−log4(w−1)=2 2\log_{4}(w + 3) - \log_{4}(w - 1) = 2 2log4(w+3)−log4(w−1)=2Practise 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.
