求解一个定积分,没分了帮帮忙f(t)=cost*sinwt(w为常数）,积分上限位π,下限为0,求积分f(t)dt

Question

求解一个定积分,没分了帮帮忙
f(t)=cost*sinwt(w为常数）,积分上限位π,下限为0,求积分f(t)dt

Answer 1

用积化和差
原式=1/2∫(0,π)[sin(t+wt)-sin(t-wt)]dt
=1/2[-cos(t+wt)/(1+w)+cos(t-wt)/(1-w)](0,π)
=1/2[-cos(π+wπ)/(1+w)+cos(π-wπ)/(1-w)+1/(1+w)-1/(1-w)]