In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The velocity v(t)v(t)v(t), in mm s−1\text{mm s}^{-1}mm s−1, of a microscopic probe is modeled by the function
v(t)=12tcos(3t),0≤t≤π6 v(t) = 12t \cos(3t), \quad 0 \le t \le \frac{\pi}{6} v(t)=12tcos(3t),0≤t≤6πwhere t t\,t is the time in seconds since the measurement began.
Find the total displacement of the probe over the interval 0≤t≤π6\displaystyle 0 \le t \le \frac{\pi}{6}0≤t≤6π, giving your answer in simplest form.
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.