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=∫06πR(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.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.