求教一道二重积分的题目!∫∫(D
解:∫∫ye^xydxdy
=∫dx∫ye^(xy)dy
=∫(1/x)dx∫ye^(xy)d(xy)
=∫(1/x)dx∫yde^(xy)
=∫(1/x)[ye^(xy)|-∫e^(xy)dy]dx
=∫(1/x)[2e^(2x)-(e/x)-(1/x)e^(xy)|]dx
=∫(1/x){2e^(2x)-(e/x)-[e^(2x)/x]+(e/x)}dx
=2∫(1/x)[e^(2x)]dx-∫[e^(2x)/x²]dx
=2∫(1/x)[e^(2x)]dx+∫[e^(2x)]d(1/x)
=2∫(1/x)[e^(2x)]dx+[e^(2x)/x]]|
-∫(1/x)de^(...全部
解:∫∫ye^xydxdy
=∫dx∫ye^(xy)dy
=∫(1/x)dx∫ye^(xy)d(xy)
=∫(1/x)dx∫yde^(xy)
=∫(1/x)[ye^(xy)|-∫e^(xy)dy]dx
=∫(1/x)[2e^(2x)-(e/x)-(1/x)e^(xy)|]dx
=∫(1/x){2e^(2x)-(e/x)-[e^(2x)/x]+(e/x)}dx
=2∫(1/x)[e^(2x)]dx-∫[e^(2x)/x²]dx
=2∫(1/x)[e^(2x)]dx+∫[e^(2x)]d(1/x)
=2∫(1/x)[e^(2x)]dx+[e^(2x)/x]]|
-∫(1/x)de^(2x)
=[e^(2x)/x]]|=(e^4/2)-e²。
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