计算二重积分,∫∫(√x^2+y^2)dxdy,其中D是圆形区域a^2≤x^+y^2≤b^

2024-11-07 22:35:53
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a^2≤x^+y^2≤b^2
令x=pcosa,y=psina
a≤p≤b,0≤a≤2π
∫∫√(x^2+y^2)dxdy
=∫[0,2π]da∫[a,b]p*pdp
=a[0,2π]*1/2p^2[a,b]
=π(b^2-a^2)