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.
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.