∫∫x√(x²+y²)dxdy=∫dθ∫rcosθ*r*rdr (作极坐标变换)
=∫cosθdθ∫r³dr
=[(sinθ)│]*[(r^4/4)│]
=[sin(π/2)-sin(0)]*(1^4/4-0^4/4)
=1*(1/4)
=1/4.