The gain response, GGG, of a specialized amplifier is modeled by the function G(t)=log2(4t)G(t) = \log_2(4t)G(t)=log2(4t), where ttt is the signal frequency in kHz. The table below shows values of GGG for specific frequencies recorded during a test.
t246810G3.004.004.585.005.32\begin{array}{|c|c|c|c|c|c|} \hline t & 2 & 4 & 6 & 8 & 10 \\ \hline G & 3.00 & 4.00 & 4.58 & 5.00 & 5.32 \\ \hline \end{array}tG23.0044.0064.5885.00105.32
Using the trapezium rule with all the values of GGG in the given table,
obtain an estimate for ∫210log2(4t) dt\int_{2}^{10} \log_2(4t) \, dt ∫210log2(4t)dt, giving your answer to one decimal place.
Using your answer to part (a) and making your method clear, estimate
(i) ∫210log2(64t3)5 dt\int_{2}^{10} \frac{\log_2(64t^3)}{5} \, dt ∫2105log2(64t3)dt
(ii) ∫210log2(16t) dt\int_{2}^{10} \log_2 \left(\frac{16}{t}\right) \, dt ∫210log2(t16)dt
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.
