The torque τ\tauτ, in Newton-meters, applied to a rotating flywheel is modeled by τ(t)=12tsin(2t)\tau(t) = 12t \sin(2t)τ(t)=12tsin(2t), where ttt is the time in seconds. The total angular impulse JJJ delivered between t=π6t = \frac{\pi}{6}t=6π and t=π4t = \frac{\pi}{4}t=4π is defined by the integral:
J=∫π6π412tsin(2t) dt J = \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} 12t \sin(2t) \, dt J=∫6π4π12tsin(2t)dtGiven that J=aπ+bJ = a\pi + bJ=aπ+b, determine the exact value of the constant aaa and the exact value of the constant bbb.
Fully justify your answer.
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.
