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.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
