Alright, so doing the integration here's what I get:
1/2\int e^{-t/50}sin(t)dt
u=e^{-t/50},du=-1/50e^{-t/50},dv=sin(t)dt,v=-cos(t)
1/2\int e^{-t/50}sin(t)dt=1/2(-e^{-t/50}cos(t)-\int 1/50e^{-t/50}cos(t)dt
u=1/50e^{-t/50},du=-1/2500e^{-t/50}dt,dv=cos(t)dt, v=sin(t)...