利用极坐标计算下列二重积分：二重符号e^（x^2+y^2）dσ,D：x^2+y^2≤4；求过程!

利用极坐标计算下列二重积分：∫∫_D e^(x² + y²) dσ,其中区域D：x² + y² ≤ 4
{ x = rcosθ
{ y = rsinθ
x² + y² = 4 ==> r = 2
x² + y² = r²cos²θ + r²sin²θ = r²
∫∫_D e^(x² + y²) dσ
= ∫(0→2π) dθ ∫(0→2) e^r² · rdr
= (1/2)∫(0→2π) dθ ∫(0→2) e^r² d(r²)
= (1/2)∫(0→2π) [e^r²] |(0→2) dθ
= (1/2)∫(0→2π) (e⁴ - 1) dθ
= (1/2)(e⁴ - 1) · [θ] |(0→2π)
= (1/2)(e⁴ - 1) · (2π - 0)
= π(e⁴ - 1)