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) dtJ = \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} 12t \sin(2t) \, dtJ=∫6π4π12tsin(2t)dt
Given 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 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.