The concentration of a certain chemical reagent, CCC, measured in mmol/L, during a reaction is modelled by the equation
C(t)=3+4log10(cost)for 0≤t≤1 C(t) = 3 + 4 \log_{10}(\cos t) \quad \text{for } 0 \le t \le 1 C(t)=3+4log10(cost)for 0≤t≤1where ttt is the time in seconds after the reaction begins.
Complete the table below for the concentration at various times, giving values of CCC to 3 decimal places.
| ttt | 0 | 0.25 | 0.5 | 0.75 | 1 |
|---|---|---|---|---|---|
| CCC | 3.000 | 2.773 | 1.931 |
Use the trapezium rule with all the values in the completed table to find an estimate for ∫01C(t) dt\int_{0}^{1} C(t) \, dt∫01C(t)dt, giving your answer to 2 decimal places.
Hence, determine an estimate for the value of
∫01(1−2log10(cost)) dt \int_{0}^{1} (1 - 2 \log_{10}(\cos t)) \, dt ∫01(1−2log10(cost))dtgiving your answer to 2 decimal places.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) 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.
