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Question 432

A high-precision sensor measures the rate of energy dissipation, R(t)R(t)R(t), in a prototype circuit over the interval 0≤t≤π60 \le t \le \frac{\pi}{6}0≤t≤6π​ seconds. The rate is modeled by the function:

R(t)=(3t−1)cos⁡(3t) R(t) = (3t - 1) \cos(3t) R(t)=(3t−1)cos(3t)

Given that the total energy dissipated, E=∫0π6R(t) dtE = \int_{0}^{\frac{\pi}{6}} R(t) \, dtE=∫06π​​R(t)dt, can be expressed in the form aπ+ba\pi + baπ+b, find the exact value of aaa and the exact value of bbb.

Fully justify your answer.

[6]
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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