高等数学,定积分,怎么化简的?入是怎么变的?

2024-12-03 19:35:30
推荐回答(2个)
回答1:

换元法, 令 \lambda x=t

回答2:

令 λx = t, 则 x = t/λ, dx = dt/λ,
原积分 I = ∫<0, +∞> t^2e^(-t)dt/λ = (1/λ) ∫<0, +∞> t^2e^(-t)dt
= (-1/λ) ∫<0, +∞> t^2de^(-t)
= (-1/λ){[t^2/e^t]<0, +∞> - 2∫<0, +∞> te^(-t)dt}
= (-1/λ)[0 + 2∫<0, +∞> tde^(-t)]
= (-2/λ){[t/e^t]<0, +∞> - ∫<0, +∞>e^(-t)dt}
= (-2/λ){0 +[e^(-t)]<0, +∞>} = 2/λ