In an exercise with included solution I can't understand how integrating sin^2(ωt) gives T(period)/2 [itex]\int[/itex]sin^2(ωt)dt = Period/2 I posted the whole problem below, because I had more doubts, but understood them typing up the problem. I appreciate any help. YOU CAN SKIP THE PROBLEM The probelm A circular coil, r=10 and Ω=1.5Ω, rotates around its diameter with a constant ω0 in a uniform and constant magnetic field B that forms an angle of θ=∏/3 with the axis of rotation of the coil. Knowing that the maximum current Imax=0.15A, and that the component of B parallel to the axis of rotation is Bparall=1.0T, find 1) intensity of B 2) angular velocity ω0 of the coil 3) energy needed per rotation to keep the angular velocity ω0 The solution included on teh book my problem in in red 1) B=Bparallel/cosθ=2Bparallel=2.0T I did the same, so no problem here. Bperp(responsible for the current in the coil)=Bparallel*tanθ=Bparallel√3 2) fem=-dphi/dt=∏*r^2*ω*Bperp*sin(ωt), max fem when sin(ωt)=1, ω0=R*I/(∏*r^2*Bperp) 3)To get the work, i integrate over one turn, so over the period T=2∏/ω W= [itex]\int[/itex]R*I^2*dt = R*Imax^2[itex]\int[/itex]sin^2(ωt)dt = R*I^2*Period/2 I don't get how do you integrate sin^2(wt) and get T/2?