∫xe^xydxdy怎么求,0≤X≤1,-1≤y≤0

Answer 1

∫∫ xe^(xy) dxdy
先积y
=∫[0→1]dx∫[-1→0] xe^(xy) dy
=∫[0→1]dx∫[-1→0] e^(xy) d(xy)
=∫[0→1] e^(xy) |[-1→0] dx
=∫[0→1] (1 - e^(-x) dx
=x + e^(-x) |[0→1]
=1 + 1/e - 1
=1/e
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