不定积分三角函数换元问题

2024-12-23 10:16:27
推荐回答(2个)
回答1:

x=sint,t∈[-π/2,π/2]
∫√(1-x²)dx
=∫costdsint
=∫cos²tdt
=tcos²t+∫sin2tdt
=tcos²t-cos2t/2+c
=t-tsin²t+sin²t-1/2+c
=(1-x²)arcsinx+x²+c'

回答2:

(1-x^2)^1/2时,设x=sect太麻烦
应设x=sint (-π/2,π/2)
或x=cost (π,0) 方便
计算就不用说了