A robotic arm's angular velocity ω\omegaω (in rad s−1^{-1}−1) over the interval 0≤t≤π0 \le t \le \pi0≤t≤π is modelled by the function
ω(t)=tcos(12t)\omega(t) = t \cos\left(\frac{1}{2}t\right)ω(t)=tcos(21t)
where ttt is the time in seconds.
Show that the total angular displacement of the arm between t=0t = 0t=0 and t=πt = \pit=π is (2π−4)(2\pi - 4)(2π−4) radians.
Practise Edexcel A Level Maths 11.6 Integration by Parts with exam-style questions for A Level Maths. 52 questions, 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.