一道高数重积分题目

2025-05-15 02:20:02
推荐回答(2个)
回答1:

回答2:

∫(0→1)dx∫(0→x) [(x-y)^(a-1)]f(y)dy
=∫(0→1)dy∫(y→1) [(x-y)^(a-1)]f(y)dx,对x积分的原函数是f(y)×1/a(x-y)^a
=∫(0→1) f(y)×1/a(1-y)^a dy,换元y=1-z
=1/a∫(0→1)z^af(1-z) dz

=1/a∫(0→1)y^af(1-y) dy