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.
119 exam-style questions on CCEA A Level Maths 3.6.4 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.