a2n-1= 011cos[(2n-1)π2t]dt+12-t+2cos[(2n-1)π2t]dt
Haciendo
u=-t+2 , dv= cos2n-1π2tdt du=-dt , v=2π(2n-1) sin2n-1π2t a2n-1=2π(2n-1) sin2n-1π2t 01+2(-t+2)π(2n-1) sin2n-1π2t- 4π2(2n-1)2 cos2n-1π2t12 a2n-1=- 4π2(2n-1)2 cos2n-1π , como cos2n-1π=-1 , a2n-1=4π2(2n-1)2 b2n-1= 4T0T2ftsin[2n-1w0t]dt=02ftsin[(2n-1)π2t]dt b2n-1= 011sin[(2n-1)π2t]dt+12-t+2sin[(2n-1)π2t]dt Haciendo u=-t+2 , dv= sin[(2n-1)π2t]dt du=-dt , v=-2π(2n-1) cos2n-1π2t b2n-1=-2π(2n-1) cos2n-1π2t 01+-2(-t+2)π(2n-1) cos2n-1π2t- 4π22n-12 sin2n-1π2t 12 b2n-1=2π(2n-1)+4π22n-12 sin2n-1π2 , como sin2n-1π2=-(-1)n b2n-1=2π(2n-1)-4(-1)nπ22n-12 ft=n=1∞[a2n-1cos2n-1w0t+ b2n-1 sin[2n-1w0t]]