答：π (e - 1)极坐标化简x = rcosθy = rsinθx²+y²=r²,0≤r≤1,0≤θ≤2π∫∫_(D) e^(x²+y²) dxdy= ∫(0,2π) dθ ∫(0,1) e^r² * r dr= (2π)∫(0,1) e^r² d(r²)/2= π * [e^r²](0,1)= π * (e^1 - e^0)= π (e - 1)
