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 Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
