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Question 620

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(21​t)

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.

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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