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.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.