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.
