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.
52 exam-style questions on Edexcel A Level Maths 11.6 Integration by Parts. Each one has a worked solution and a mark scheme showing where the marks go.