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Question 540

The gain response, GGG, of a specialized amplifier is modeled by the function G(t)=log⁡2(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}tG​23.00​44.00​64.58​85.00​105.32​​

Using the trapezium rule with all the values of GGG in the given table,

a.

obtain an estimate for ∫210log⁡2(4t) dt\int_{2}^{10} \log_2(4t) \, dt ∫210​log2​(4t)dt, giving your answer to one decimal place.

[4]
b.

Using your answer to part (a) and making your method clear, estimate

(i) ∫210log⁡2(64t3)5 dt\int_{2}^{10} \frac{\log_2(64t^3)}{5} \, dt ∫210​5log2​(64t3)​dt

(ii) ∫210log⁡2(16t) dt\int_{2}^{10} \log_2 \left(\frac{16}{t}\right) \, dt ∫210​log2​(t16​)dt

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

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.

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