计算二重积分∫∫sin√(x2 y2)dxdy.积分区域为D.其中D:x2+y2≤1

2024-11-08 23:10:52
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∫D∫sin√(x^2+y^2)dxdy
=∫(0,2π)dθ∫(0,1)r^2dr
=∫(0,2π)[1/3r^3](0,1)dθ
=1/3∫(0,2π)[6π^3-0^3]dθ
=2π^3[θ](0,2π)
=2π^3(2π-0)
=4π^4