这个积分怎么求?

2025-03-21 00:43:21
推荐回答(1个)
回答1:

∫[0:θ] [x·n(θ-x)ⁿ⁻¹/θⁿ]dx
=-(1/θⁿ)∫[0:θ]xd[(θ-x)ⁿ]
=-(1/θⁿ)x(θ-x)ⁿ|[0:θ]+(1/θⁿ)∫[0:θ](θ-x)ⁿdx
=(1/θⁿ)[0·(θ-0)ⁿ-θ·(θ-θ)ⁿ]-[1/ (n+1)θⁿ](θ-x)ⁿ⁺¹|[0:θ]
=[1/ (n+1)θⁿ][(θ-0)ⁿ⁺¹-(θ-θ)ⁿ⁺¹]
=θ/(n+1)